What does the solution to a system of two linear equations, such as $y = 2x + 1$ and $y = -x + 4$, represent on a Cartesian plane?
The slope of the steeper line.
The point where the lines intersect the x-axis.
The point of intersection of the two lines.
The point where both lines intersect the y-axis.
Which of the following ordered pairs $(x, y)$ is the solution to the system of linear equations below?
$3x - y = 7$
$x + 2y = 7$
$(-1, 4)$
$(2, -1)$
$(1, 3)$
$(3, 2)$
A system of two linear equations in two variables has no solution. What must be true about the graphs of these two equations?
The lines are perpendicular.
The lines intersect at exactly one point.
The lines are parallel.
The lines are identical (coinciding).
The sum of the ages of a father and his son is 50. The father is 26 years older than his son. If $f$ represents the father's age and $s$ represents the son's age, which system of equations correctly models this situation?
$fs = 50$ \ $f = s + 26$
$f + s = 50$ \ $f - s = 26$
$f - s = 50$ \ $f + s = 26$
$f + s = 50$ \ $f + s = 26$
Consider the system of equations:
$y = 2x + 3$
$4x - 2y = k$
For which value of $k$ will this system have infinitely many solutions?
$k = 3$
$k = -6$
$k = 6$
$k = -3$
Solve the following system of equations using the substitution method: $x + 3y = 7$ $2x - y = 0$
$x = -1, y = -2$
$x = 1, y = 2$
$x = 2, y = 1$
$x = 4, y = 1$
Find the solution $(x, y)$ for the simultaneous equations: $x = 4y + 1$ $2x - 3y = 12$
$(2, 9)$
$(7, 2)$
$(9, 2)$
$(0, -4)$
The sum of two numbers is 30. The larger number is 3 more than the smaller number. What are the two numbers?
7.5 and 22.5
13 and 17
12 and 18
13.5 and 16.5
What is the point of intersection $(x, y)$ for the lines defined by the equations $x - y = 3$ and $3x + 4y = 23$?
$(5, 2)$
$(1, 5)$
$(7, 4)$
$(3, 0)$
Consider the system of linear equations: $y = 2x + 3$ $4x - 2y = 1$
What is the solution to this system?
No solution
Infinitely many solutions
$(0, 3)$
Solve the following system of linear equations by elimination:
$3x + y = 10$
$2x - y = 5$
$x=3, y=-1$
$x=1, y=7$
$x=5, y=-5$
$x=3, y=1$
Find the solution to the system of equations:
$5a + 2b = 24$
$3a + 2b = 16$
$a=5, b=-0.5$
$a=2, b=7$
$a=4, b=2$
$a=4, b=-2$
$4x - 3y = 11$
$2x + 3y = 1$
To solve this system using the elimination method, what is the most direct and efficient first step?
Subtract the second equation from the first.
Rearrange the first equation to solve for $x$.
Multiply the second equation by 2.
Add the two equations together.
What is the solution for the system of equations below?
$7m = 22 + 3n$
$5m + 3n = 14$
$m=3, n=-\frac{1}{3}$
$m=3, n=\frac{1}{3}$
$m=4, n=-2$
$m=3, n=-1$
What is the primary goal of the first step (addition or subtraction) when using the elimination method to solve a system of two linear equations?
To find the value of one of the variables directly from the sum or difference.
To simplify the system by dividing both equations by their greatest common factor.
To transform the two-variable system into a single equation with only one variable.
To ensure the coefficients of both variables are additive inverses.
Consider the system of linear equations: \begin{cases} 3x + 4y = 11 \ x - 2y = -3 \end{cases} To solve this system by elimination, what is the most efficient first step to eliminate the variable $y$?
Multiply the second equation by 3, then subtract the new equation from the first equation.
Add the two equations together without any multiplication.
Multiply the first equation by 2, then subtract the second equation from the new equation.
Multiply the second equation by 2, then add the new equation to the first equation.
Solve the following system of linear equations: \begin{cases} 2x + 3y = 1 \ 3x + 4y = 1 \end{cases}
$x = -1, y = 1$
$x = 1, y = -1$
$x = -7, y = 5$
$x = 5, y = -3$
Which of the following describes a correct procedure to begin solving the system of equations? \begin{cases} 3x + 5y = 1 \ 5x + 3y = 7 \end{cases}
Multiply the first equation by 5 and add it to the second equation without changing the second equation.
Multiply the first equation by 3, the second by 5, and subtract the new second equation from the new first equation.
Multiply the first equation by -3, the second by 5, and subtract the resulting equations.
Multiply the first equation by 5, the second by 3, and add the resulting equations.
At a bookstore, the total cost for 2 hardcover books and 3 paperback books is 81 dollars. The total cost for 3 hardcover books and 2 paperback books is 84 dollars. What is the cost of one hardcover book?
21 dollars
15 dollars
25 dollars
18 dollars
Given the system of equations \begin{cases} 4a - 3b = 18 \ 3a + 2b = 5 \end{cases} what is the value of the expression $a - b$?
1
5
-1
3
Which of the following systems of linear equations has exactly one solution?
$x - 2y = 6$ and $-2x + 4y = -5$
$y = 3x - 2$ and $y = 3x + 5$
$2x + y = 4$ and $4x + 2y = 8$
$y = -2x + 1$ and $y = x - 4$
Consider the system of equations: $4x - 2y = 10$ and $y = 2x - 3$. How many solutions does this system have?
One solution
Infinite solutions
It is impossible to determine
For a system of two linear equations to have an infinite number of solutions, which condition must be true?
The lines must have different gradients.
The lines must have the same gradient but different y-intercepts.
The lines must have the same gradient and the same y-intercept.
The lines must be perpendicular.
For what value of $k$ will the system of equations below have no solution? \ $3x + 5y = 9$ \ $kx + 10y = 12$
$k = 5$
$k = 1.5$
The system of equations $x - 7y = 2$ and $3x - 21y = 6$ is best described as:
Inconsistent, with no solution.
Independent, with one solution.
Dependent, with infinite solutions.
A system with perpendicular lines.
Which of the following systems of linear equations is inconsistent, meaning it has no solution?
$y = 2x + 1$ and $y = -2x + 1$
$y = x + 2$ and $y = 2x + 1$
$y = 4x - 3$ and $y = 4x - 3$
$y = 5x + 7$ and $y = 5x - 1$
A system of linear equations is said to be inconsistent if its graph consists of parallel lines. Which of the following systems is inconsistent?
$3x - 2y = 4$ and $6x - 4y = 8$
$x - 3y = 7$ and $2x - 6y = 10$
$x + y = 5$ and $2x - y = 1$
$2x + 5y = 10$ and $x - y = 3$
Consider the system of equations: \begin{cases} kx + 2y = 4 \ 6x + 4y = 7 \end{cases} For what value of $k$ will this system be inconsistent?
$k = 2$
A system of linear equations representing two distinct lines has no solution. Which of the following statements must be true about these two lines?
They have the same gradient and the same y-intercept.
They have the same y-intercept but different gradients.
They have the same gradient but different y-intercepts.
They are perpendicular to each other.
The total cost, $C$ in dollars, for two different catering companies is based on the number of guests, $g$. Company A's cost is modelled by the equation $C = 30g + 500$. Company B's cost is modelled by $C = 30g + 400$. Which statement best describes the possibility of the costs being identical?
The costs are identical only if there are 0 guests.
The costs are identical if there are 10 guests.
Company B is always more expensive than Company A, so the costs are never identical.
Company A is always more expensive than Company B, so the costs are never identical.
Which of the following systems of linear equations is a dependent system, meaning its graph consists of coincident lines?
$x + y = 5$ and $x - y = 5$
$3x - y = 7$ and $6x - 2y = 14$
$5x + 2y = 3$ and $5x + 2y = 4$
$2x + 4y = 10$ and $x + 2y = 8$
A system of equations is shown below:
How would you describe this system?
Dependent system with infinitely many solutions.
Inconsistent system with no solutions.
A non-linear system.
Independent system with one solution.
For what value of $k$ will the following system of linear equations be dependent?
$5x + 2y = 4$ $15x + ky = 12$
$k=5$
$k=6$
$k=2$
$k=3$
When solving a system of two linear equations using an algebraic method such as substitution or elimination, you arrive at the true statement $0 = 0$. What does this result signify about the system?
An error must have been made in the calculation.
The system has exactly one solution at the origin $(0,0)$.
The system is dependent and its graph consists of coincident lines.
The system is inconsistent and its graph consists of parallel lines.
Consider the system of equations: $4x = 8 - 2y$ and $3y + 6x - 12 = 0$. Which statement accurately describes the graphical representation of this system?
The lines are coincident (the same line).
The lines are parallel and distinct.
The lines intersect at a single point.
Consider the following system of simultaneous equations:
$y = 4x - 7$
$3x + 2y = 16$
Which of the following describes the most efficient method to solve this system?
Substitution, because the variable $y$ is already isolated in the first equation.
Elimination, because you can multiply the first equation by 2 to match the $y$ coefficients.
Graphical method, because the y-intercept of the first equation is an integer.
Elimination, because the coefficients of $x$ (4 and 3) are close in value.
To solve the system of equations below, which method would be the most efficient first step?
$5a + 2b = 11$
$7a - 2b = 1$
Elimination, by adding the two equations together.
Substitution, by isolating $a$ in the first equation, which gives $a = \frac{11-2b}{5}$.
Elimination, by subtracting the second equation from the first.
Substitution, by rearranging the second equation to make $b$ the subject.
Analyse the following system of linear equations:
Equation 1: $3x + 5y = 9$
Equation 2: $x - 4y = 10$
What is the most direct method to begin solving this system?
Elimination, by multiplying Equation 2 by -3 and adding it to Equation 1.
Elimination, by multiplying Equation 1 by 4 and Equation 2 by 5 to eliminate $y$.
Substitution, by rearranging Equation 2 to $x = 10 + 4y$ and substituting into Equation 1.
Substitution, by rearranging Equation 1 to $y = \frac{9-3x}{5}$ and substituting into Equation 2.
Consider the system:
$4p + 3q = 15$
$12p - 5q = -3$
Which of the following represents the most efficient strategy to solve for $p$ and $q$?
Substitution, because it avoids working with large numbers.
Elimination, by multiplying the first equation by 5 and the second equation by 3 to eliminate $q$.
Elimination, by multiplying the first equation by 3 to make the coefficients of $p$ match.
Graphical method, because the gradients are different, which guarantees one solution.
You are given the following system of equations:
$3m + 4n = 2$
$5m + 7n = 1$
Neither substitution nor elimination offers an immediately simple solution. When comparing the two algebraic methods, why is elimination generally considered more efficient in this specific case?
Because both equations are in the form $Ax+By=C$, which is only suitable for the elimination method.
Because the constants (2 and 1) are small, making substitution easier to manage.
Because elimination can be done by subtracting the first equation from the second.
Because substitution would require rearranging an equation, which immediately introduces fractions.
A school play sold a total of 250 tickets. An adult ticket costs 15 dollars and a student ticket costs 10 dollars. The total revenue from ticket sales was 3125 dollars. Let $a$ represent the number of adult tickets and $s$ represent the number of student tickets. Which system of equations correctly represents this situation?
$15a + s = 250$ \ $a + 10s = 3125$
$a + s = 250$ \ $10a + 15s = 3125$
$a + s = 250$ \ $15a + 10s = 3125$
$a + s = 3125$ \ $15a + 10s = 250$
A chemist wants to create a 100 mL solution that is 25% acid. She mixes a solution that is 10% acid with another solution that is 40% acid. Let $x$ be the volume of the 10% solution and $y$ be the volume of the 40% solution. Which system of equations can be used to find the volume of each solution needed?
$x + y = 25$ \ $0.10x + 0.40y = 100$
$x + y = 100$ \ $0.10x + 0.40y = 100$
$x + y = 100$ \ $0.10x + 0.40y = 25$
$x + y = 100$ \ $10x + 40y = 25$
The perimeter of a rectangular garden is 54 metres. The length is 3 metres more than twice the width. Let $l$ be the length and $w$ be the width of the garden. Which system of equations models the dimensions of the garden?
$2l + 2w = 54$ \ $l = 2w + 3$
$2l + 2w = 54$ \ $w = 2l + 3$
$l + w = 54$ \ $l = 2w + 3$
$2l + 2w = 54$ \ $l = 2w - 3$
Maya invested a total of 10000 dollars in two different accounts. One account earns 4% annual interest, and the other earns 6% annual interest. After one year, she earned a total of 520 dollars in interest. Let $x$ be the amount invested at 4% and $y$ be the amount invested at 6%. Which system of equations represents Maya's investments?
$0.04x + 0.06y = 10000$ \ $x + y = 520$
$x + y = 10000$ \ $4x + 6y = 520$
$x + y = 520$ \ $0.04x + 0.06y = 10000$
$x + y = 10000$ \ $0.04x + 0.06y = 520$
A parking lot contains a total of 60 vehicles, consisting only of cars and motorcycles. The total number of wheels in the parking lot is 190. (Assume cars have 4 wheels and motorcycles have 2 wheels). Let $c$ be the number of cars and $m$ be the number of motorcycles. Which system of equations can be used to determine the number of cars and motorcycles?
$c + m = 60$ \ $4c + 2m = 190$
$c - m = 60$ \ $4c + 2m = 190$
$c + m = 60$ \ $2c + 4m = 190$
$c + m = 190$ \ $4c + 2m = 60$
The sum of two distinct numbers is 42 and their difference is 16. What is the value of the larger number?
$26$
$16$
$29$
$13$
A school canteen sells two types of sandwiches: vegetarian and chicken. On a particular day, a total of 120 sandwiches were sold. A vegetarian sandwich costs 5 dollars and a chicken sandwich costs 7 dollars. If the total sales for the day amounted to 720 dollars, how many chicken sandwiches were sold?
$50$
$70$
$80$
$60$
The sum of the digits of a two-digit number is 11. When the digits are reversed, the new number is 45 less than the original number. What is the original number?
$38$
$83$
$74$
$47$
At a farm, there are only sheep and chickens. You count 35 heads and 94 legs in total. How many sheep are on the farm?
$12$
$23$
$15$
$25$
A mother is currently four times as old as her daughter. In 6 years, the mother will be three times as old as her daughter. What is the sum of their current ages?
$48$
$72$
$54$
Solve the following system of linear equations:
$0.4x + 0.3y = 1.7$
$0.7x - 0.2y = 0.8$
$x=0, y=-4$
$x=2, y=3$
$x=5, y=-1$
$x=3, y=2$
$\frac{1}{2}x + \frac{1}{3}y = 4$
$\frac{1}{4}x - \frac{1}{6}y = 0$
$x=4, y=6$
$x=8, y=0$
$x=6, y=4$
Solve the system of equations below, which includes both a decimal and fractions.
$y = 0.5x + 1$
$\frac{1}{4}x - \frac{1}{3}y = -1$
$x=-8, y=-3$
$x=8, y=5$
$x=-16, y=-7$
$x=-3, y=-8$
A coffee shop creates a blend using two types of beans. Arabica beans cost 4.50 dollars per kg, and Robusta beans cost 3.00 dollars per kg. A 10 kg bag of the blend costs a total of 39 dollars. Which system of equations correctly represents this situation, where $a$ is the number of kilograms of Arabica and $r$ is the number of kilograms of Robusta?
$a + r = 10$ and $3a + 4.5r = 39$
$a + r = 39$ and $4.5a + 3r = 10$
$a \times r = 10$ and $4.5a + 3r = 39$
$a + r = 10$ and $4.5a + 3r = 39$
Determine the solution for the following system of equations:
$\frac{x+y}{4} - \frac{x-y}{3} = 1$
$\frac{1}{2}x + y = 1$
$x = \frac{4}{3}, y = \frac{1}{3}$
$x = -26, y = 14$
$x = \frac{14}{9}, y = -\frac{10}{9}$
$x = -\frac{10}{9}, y = \frac{14}{9}$
Solve the inequality $-4x > 20$.
$x > -5$
$x > 5$
$x < 5$
$x < -5$
Find the solution set for the inequality $10 - 3x \le 22$.
$x \ge -4$
$x \ge 4$
$x \le -4$
$x \le 4$
Under which of the following conditions must an inequality symbol always be reversed?
Any time there is a negative number next to the variable.
When multiplying or dividing both sides of the inequality by a negative number.
When subtracting a number from both sides, resulting in a negative number.
When adding a negative number to both sides of the inequality.
Which inequality is equivalent to $3x - 8 \ge 7x + 12$?
$x \ge -5$
$x \le 5$
$x \le -5$
$x \ge 5$
An inequality is solved as follows:
Step 1: $-5(x - 2) > 25$
Step 2: $x - 2 < -5$
Step 3: $x < -3$
Identify the reasoning that justifies the change from Step 1 to Step 2.
Adding 5 to both sides of the inequality.
Dividing both sides by $-5$ and reversing the inequality symbol.
Distributing the $-5$ to both terms inside the parentheses.
Dividing both sides by $-5$ and keeping the inequality symbol the same.
Solve the inequality: $2(x - 4) + 3x < 7$.
$x < 3$
$x > 3$
$x < 1$
$x > 1$
Which inequality represents the solution to $7x - 5 \ge 4x + 10$?
$x \ge \frac{5}{3}$
Solve for $m$: $12 - 5m > 32$.
$m < 4$
$m < -4$
$m > 4$
$m > -4$
Find the solution set for the inequality $3(p + 1) - 5p \le 2(p + 7)$.
$p \le \frac{11}{4}$
$p \ge -\frac{11}{2}$
$p \le -\frac{11}{4}$
$p \ge -\frac{11}{4}$
What is the solution to the inequality $\frac{y - 4}{2} > \frac{3y - 2}{5}$?
$y < -18$
$y > -16$
$y > 16$
$y < -16$
Which of the following inequalities is the solution to $7x - 5 > 4x + 7$?
$x < \frac{2}{11}$
$x > \frac{2}{3}$
$x < 4$
$x > 4$
Solve the inequality: $5 - 3a \leq 2a + 20$.
$a \geq -3$
$a \geq 3$
$a \leq -3$
$a \leq 3$
Find the solution set for the inequality $4(k - 1) < 7(k + 2)$.
$k < -6$
$k < 6$
$k > -6$
$k > 6$
Solve for $m$: $9m - 4 \geq -2(m + 15)$.
$m \leq -\frac{34}{7}$
$m \geq -\frac{26}{11}$
$m \geq -2$
$m \leq -2$
What is the solution to the inequality $\frac{1}{3}y + 5 > \frac{3}{4}y - 5$?
$y < 0$
$y < 24$
$y > 24$
$y > 12$
A telecommunications company offers a mobile phone plan that costs 25 dollars per month plus 0.10 dollars for each gigabyte (GB) of data used. If you want your total monthly bill to be at most 40 dollars, what is the maximum number of gigabytes of data you can use? Let $g$ be the number of gigabytes.
$g \ge 150$
$g \le 150$
$g \le 15$
$g \ge 25$
To pass a history course, a student needs an average of at least 70 on four exams. The student's scores on the first three exams are 65, 72, and 68. What is the minimum score the student must achieve on the fourth exam to pass the course? Let $x$ be the score on the fourth exam.
$x \ge 72$
$x \ge 75$
$x \ge 70$
$x \ge 65$
A small business owner is producing handcrafted bracelets. The fixed cost for equipment is 120 dollars, and the cost of materials per bracelet is 3 dollars. If each bracelet is sold for 15 dollars, what is the minimum number of bracelets the owner must sell to make a profit of at least 300 dollars?
20 bracelets
25 bracelets
34 bracelets
35 bracelets
The length of a rectangular garden is 4 metres longer than its width, $w$. The perimeter of the garden must be no more than 60 metres. Which inequality correctly represents the possible values for the width?
$w \le 28$
$w \ge 13$
$w \le 14$
$w \le 13$
A delivery truck can carry a maximum load of 1500 kg. It is loaded with 10 identical boxes, and the driver, who weighs 80 kg, is in the truck. If the total weight of the truck with the driver and boxes must not exceed the maximum load, what is the maximum possible weight, $x$, of each box?
$x \le 142 \text{ kg}$
$x \le 158 \text{ kg}$
$x \le 150 \text{ kg}$
$x \ge 142 \text{ kg}$
Which of the following is the solution to the compound inequality $-5 \le 2x - 1 < 7$?
$x \le -2$ or $x > 4$
$x < -2$ or $x \ge 4$
$-2 \le x < 4$
$-2 < x \le 4$
Find the solution set for the compound inequality: $3x + 4 \le -2$ or $5x - 8 > 7$.
$-2 \le x < 3$
$x \le -2$ or $x > 3$
$x \ge -2$ and $x < 3$
The solution set is empty.
A number line graph shows a solution set with a closed circle at $-1$ and shading to the left, and an open circle at $4$ and shading to the right. Which compound inequality does this graph represent?
$x \le -1$ or $x > 4$
$-1 \le x < 4$
$x < -1$ or $x \ge 4$
$x \ge -1$ or $x < 4$
A chemical process requires the temperature, $T$ (in degrees Celsius), to be strictly greater than $10^{\circ}C$ and less than or equal to $35^{\circ}C$. Which inequality represents the valid range for $T$?
$T > 10$ or $T \le 35$
$10 \le T < 35$
$T < 10$ or $T \ge 35$
$10 < T \le 35$
In the context of sets, the solution to a compound inequality using 'and' corresponds to the __________ of the individual solution sets, while 'or' corresponds to the __________.
union; intersection
complement; subset
subset; complement
intersection; union
Solve for $x$: $x + 2 > 5$ and $3x \le 18$.
$x > 3$ or $x \le 6$
$3 < x \le 6$
$x < 3$ or $x \ge 6$
$3 \le x < 6$
Which inequality represents the solution to $-3 \le 2x + 1 < 9$?
$x \ge -2$ or $x < 4$
$-1 \le x < 5$
Find the solution set for the compound inequality: $5 - x > 2$ and $2x + 1 \ge 7$.
$x = 3$
$x \ge 3$
A number $n$ is such that it is greater than $-5$ and no more than $2$. At the same time, $n$ must be less than $0$. Which compound inequality correctly describes all possible values of $n$?
$-5 < n < 0$
$-5 < n \le 2$
$n < 0$
$0 < n \le 2$
What is the solution to the compound inequality $-4x + 7 > -1$ and $3x - 5 > -14$?
$x > -3$ or $x < 2$
$x < -3$ or $x > 2$
$-3 < x < 2$
$-2 < x < 3$
Which of the following describes the correct graph of the compound inequality $x > -4$ and $x \le 2$?
A closed circle at $2$, an open circle at $-4$, and shading in opposite directions away from the circles.
Closed circles at both $-4$ and $2$, and the line segment shaded between them.
A closed circle at $2$, an open circle at $-4$, and the line segment shaded between them.
An open circle at $2$, a closed circle at $-4$, and the line segment shaded between them.
A number line shows a graph with an open circle on $-1$, a closed circle on $6$, and the segment between them is shaded. Which compound inequality does this graph represent?
$x > -1$ or $x \le 6$
$-1 < x \le 6$
$-1 \le x < 6$
$x < -1$ or $x \ge 6$
Which of the following is the correct graphical representation of the solution to the inequality $-5 \le 2x + 1 < 7$?
Closed circles at both $-3$ and $3$, and the line segment shaded between them.
A closed circle at $-6$, an open circle at $6$, and the line segment shaded between them.
An open circle at $-3$, a closed circle at $3$, and the line segment shaded between them.
A closed circle at $-3$, an open circle at $3$, and the line segment shaded between them.
The acceptable range for the pH of a swimming pool is greater than or equal to $7.2$ and less than $7.8$. Which number line correctly models this situation?
An open circle at $7.2$, a closed circle at $7.8$, and shading in between.
Open circles at both $7.2$ and $7.8$, and shading in between.
Closed circles at both $7.2$ and $7.8$, and shading in between.
A closed circle at $7.2$, an open circle at $7.8$, and shading in between.
What is the correct graph for the solution to the compound inequality $-7 \le -3x + 2 < 5$?
An open circle at $-1$, a closed circle at $3$, and the line segment shaded between them.
An open circle at $-1$, a closed circle at $3$, and shading in opposite directions away from the circles.
An open circle at $-3$, a closed circle at $1$, and the line segment shaded between them.
A closed circle at $-1$, an open circle at $3$, and the line segment shaded between them.
Which of the following correctly represents the solution set for the compound inequality $x < -3$ or $x \ge 1$?
$-3 < x \le 1$
$x < -3$ or $x \ge 1$
$x \le -3$ or $x > 1$
$x$ is any real number.
Find the solution set for the compound inequality $2x + 1 > 9$ or $x - 3 < 0$.
$x > 4$ or $x < 3$
$x > 3$ or $x < 4$
$3 < x < 4$
Solve the compound inequality: $3x - 5 \ge 10$ or $-4x + 2 > 10$.
$x < -2$ or $x \ge 5$
$x > -2$ or $x \ge 5$
$-2 < x \le 5$
What is the most simplified solution to the compound inequality $k + 5 > 7$ or $4k > -12$?
$k > 2$ or $k > -3$
$-3 < k < 2$
$k > 2$
$k > -3$
Solve for $m$: $3(m-1) \le -15$ or $\frac{m}{2} + 5 > 7$.
$-4 \le m < 4$
$m \le -6$ or $m > 4$
$m \le -4$ or $m > 4$
$m \ge -4$ or $m < 4$
Which number line correctly represents the solution to the compound inequality $x \le -4$ or $x > 1$?
The entire number line is shaded.
An open circle on -4 with the line shaded to the left, and a closed circle on 1 with the line shaded to the right.
A closed circle on -4 and an open circle on 1, with the line shaded between them.
A closed circle on -4 with the line shaded to the right, and an open circle on 1 with the line shaded to the left.
A closed circle on -4 with the line shaded to the left, and an open circle on 1 with the line shaded to the right.
The graph on a number line shows a closed circle at 2 with shading to the right, and an open circle at -3 with shading to the left. Which compound inequality does this graph represent?
$x < -3$ and $x \ge 2$
$x < -3$ or $x \ge 2$
$-3 < x \le 2$
$x > -3$ or $x \le 2$
$x \le -3$ or $x > 2$
What is the solution set for the compound inequality $4x + 7 < -1$ or $10 - 2x \le 4$?
$x < -2$ or $x \ge 3$
The solution is all real numbers.
$x < -2$ or $x \le 3$
$-2 > x \ge 3$
$x > -2$ or $x \ge 3$
Which of the following values is NOT a solution to the compound inequality $a \le 0$ or $a > 5$?
$-0.01$
$0$
$-10$
$5$
$6$
Solve the compound inequality: $\frac{w}{3} + 1 \ge 3$ or $5 - w > 7$. Which description matches its graph?
A closed circle at -2 shaded to the left, and an open circle at 6 shaded to the right.
An open circle at -2 shaded to the right, and a closed circle at 6 shaded to the left.
An open circle at -2 shaded to the left, and a closed circle at 6 shaded to the right.
An open circle at -2 shaded to the left, and a closed circle at 6 shaded to the left.
The region between an open circle at -2 and a closed circle at 6 is shaded.
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