Solve for $x$: $-5 \le 2x + 1 < 7$.
$[-3, 3)$
$(-3, 3]$
$[-3, 3]$
$(-3, 3)$
$(-\infty, -3] \cup [3, \infty)$
Find the solution set for $3x - 4 < -10$ or $2x + 5 > 11$.
$(-\infty, -2) \cup (3, \infty)$
$(-2, 3)$
$(-\infty, -2] \cup [3, \infty)$
$(-\infty, 3) \cup (-2, \infty)$
No solution
Solve the inequality: $1 < 7 - 2x \le 9$.
$[-1, 3)$
$(-3, 1]$
$(-1, 3]$
$(-\infty, -1] \cup (3, \infty)$
$[-1, 3]$
What is the solution set for $x + 5 < 3$ and $x - 2 > 1$?
$\emptyset$
$\mathbb{R}$
${-2, 3}$
Solve the inequality: $4x - 3 \le 9$ or $-x + 2 < 3$.
${x \mid x > -1}$
Find the solution for $\frac{1}{2}x - 1 > 2$ or $5 - \frac{1}{3}x > 4$.
$(-\infty, 3) \cup (6, \infty)$
$(3, 6)$
$(-\infty, 3)$
$(6, \infty)$
$(-\infty, 6) \cup (3, \infty)$
Solve for $x$: $-11 \le 1 - 3x \le -2$.
$[1, 4]$
$[-4, -1]$
$[4, 1]$
$(-\infty, 1] \cup [4, \infty)$
$(1, 4)$
The temperature $T$ in degrees Celsius must be kept between $15^\circ C$ and $25^\circ C$, inclusive. The temperature in Fahrenheit $F$ is given by $F = \frac{9}{5}C + 32$. Which compound inequality represents the allowed temperature range in Fahrenheit?
$59 \le F \le 77$
$15 \le F \le 25$
$47.4 \le F \le 61.4$
$F \le 59 \text{ or } F \ge 77$
$27 \le F \le 45$
Solve for $y$: $2(y - 3) + 5 \le 7$ and $4 - (y+1) > 0$.
$(-\infty, 4]$
$(3, 4]$
$(3,\infty) \cup (-\infty, 4]$
Solve: $3x + 7 < 5x - 1 < 4x + 9$.
$(4, 10)$
$(-\infty, 4) \cup (10, \infty)$
$(-10, -4)$
$(-\infty, 10)$
$(4, \infty)$
Solve the inequality: $5 - 2x > 11$ or $4x + 1 > 9$.
$(-\infty, -3) \cup (2, \infty)$
$(-3, 2)$
$(-\infty, 2) \cup (-3, \infty)$
Solve: $-\frac{2}{3} \le \frac{1}{3}(x-4) < 0$.
$[2, 4)$
$(2, 4]$
$(-4, -2]$
$(-\infty, 2] \cup [4, \infty)$
$[2, 4]$
What is the solution to the inequality $9 \le 3(x+1) \le 9$?
${2}$
$[2, \infty)$
$(-\infty, 2]$
Solve: $2x - 1 > 3$ or $x + 2 > 1$.
$(-1, \infty)$
$(2, \infty)$
$(-\infty, -1) \cup (2, \infty)$
$(-1, 2)$
Solve: $3x + 5 < 14$ and $x - 7 < -2$.
$(-\infty, 5)$
$(3, 5)$
$(-\infty, 3) \cup (-\infty, 5)$
$(5, \infty)$
Find the solution set for $|x-2| > 3$.
$(-\infty, -1) \cup (5, \infty)$
$(-1, 5)$
$(-\infty, -1] \cup [5, \infty)$
$(-5, 1)$
Find the solution set for $|2x+1| \le 5$.
$[-3, 2]$
$(-\infty, -3] \cup [2, \infty)$
$[-2, 3]$
Solve the compound inequality: $-7 < -2x - 3 \le 1$.
$[-2, 2)$
$(-2, 2]$
$(-2, 2)$
$[-2, \infty)$
$(-\infty, 2)$
Solve: $\frac{x-1}{2} > 1$ or $\frac{x+3}{4} \le 0$.
$(-\infty, -3] \cup (3, \infty)$
$(-\infty, -3]$
$(3, \infty)$
A student needs an average score of at least 80 but not more than 90 on four tests. The scores on the first three tests are 75, 82, and 88. What range of scores on the fourth test, $x$, will give the desired average?
$75 \le x \le 115$
$75 \le x \le 100$
$80 \le x \le 90$
$75 \le x \le 95$
$85 \le x \le 105$
Find the solution set for $2x - 3 \ge 7$ and $15 - x \ge 10$.
${5}$
$[5, \infty)$
$(-\infty, 5]$
Which interval represents the solution to $3(x-1) \le 12$ or $-(x+2) < -8$?
$(-\infty, 5] \cup (6, \infty)$
$(5, 6]$
$(-\infty, \infty)$
Solve for $x$: $0 \le \frac{x}{2} + 3 \le 5$.
$[-6, 4]$
$(-6, 4)$
$(-\infty, -6] \cup [4, \infty)$
$[4, -6]$
What are the integer solutions to the inequality $-1 < 2x - 5 \le 3$?
${3, 4}$
${2, 3, 4}$
${3}$
${4}$
${2, 3}$
Solve the compound inequality: $2x - 1 < x + 3 < 3x - 1$.
$(2, 4)$
$(-\infty, 2) \cup (4, \infty)$
Which inequation is represented by the graph below?
$y > 2x - 3$
$y < 2x - 3$
$y \ge 2x - 3$
$y > -2x - 3$
$y > 2x + 3$
Identify the linear inequation that corresponds to the shaded region shown in the graph.
$y < -\frac{1}{2}x + 1$
$y \ge -\frac{1}{2}x + 1$
$y \le \frac{1}{2}x + 1$
$y \le -\frac{1}{2}x + 1$
$y \le -\frac{1}{2}x - 1$
The graph shows the solution to which of the following inequations?
$y < 2$
$y \ge 2$
$x \le 2$
$y \le 2$
$y \le -2$
Which inequation correctly describes the shaded area in the coordinate plane?
$y \ge -1$
$y > 1$
$x > -1$
$y < -1$
$y > -1$
Determine the inequation that represents the graphical solution provided.
$y \le -x$
$y \ge x$
$y > -x$
$y \ge -x$
$y \le x$
Which linear inequality is represented by the graph below?
$2x + 3y \le 6$
$2x + 3y \ge 6$
$2x + 3y < 6$
$3x + 2y \le 6$
$2x - 3y \le 6$
Identify the correct linear inequality for the given graph.
$x - 4y > 8$
$x - 4y < 8$
$x - 4y \ge 8$
$x + 4y > 8$
$4x - y > 8$
The graph shows the solution set for which of the following inequalities?
$-3x - 2y > 12$
$-3x - 2y < 12$
$3x + 2y < -12$
$-3x - 2y \le 12$
$2x + 3y > -12$
Select the inequality that corresponds to the shaded region in the graph.
$x \le -3$
$x > -3$
$y \ge -3$
$x \ge -3$
$y \le -3$
Which inequality's solution is depicted by the shaded area in the coordinate plane?
$5x - 2y \ge 0$
$5x - 2y < 0$
$2x - 5y < 0$
$5x + 2y > 0$
$5x - 2y > 0$
Which of the following ordered pairs is a solution to the linear inequation $y > 3x - 4$?
$(1, -1)$
$(2, 2)$
$(0, -5)$
$(-1, -7)$
Is the point $(-2, 5)$ a solution to the inequation $2x - 3y \leq -20$?
Yes, because $-19$ is less than $-20$.
No, because $-19$ is not less than or equal to $-20$.
Yes, because substituting the point results in a true statement.
No, because the point lies on the boundary line.
It cannot be determined without a graph.
Which of the following ordered pairs is NOT a solution to the inequation $5x + 2y \geq 10$?
$(2, 0)$
$(0, 5)$
$(4, -4)$
$(3, -2)$
$(1, 2)$
Consider the inequation $y < -\frac{1}{2}x + 3$. Which point satisfies this condition?
$(0, 3)$
$(-4, 5)$
$(6, -1)$
$(4, 1)$
The admission fee for a fair is 15 dollars for children and 40 dollars for adults. An organizer wants to make at least 2000 dollars. The inequation representing this situation is $15x + 40y \geq 2000$, where $x$ is the number of children and $y$ is the number of adults. Which combination of attendees meets the goal?
(50 children, 30 adults)
(100 children, 12 adults)
(80 children, 20 adults)
(30 children, 38 adults)
(90 children, 15 adults)
Which point is a solution to the inequality $x > 4$?
$(4, 5)$
$(3, 9)$
$(4.01, -2)$
$(-5, 4)$
$(0, 0)$
An ordered pair $(a, b)$ is a solution to $b \geq -a$. Which of the following statements must be true?
$a + b \geq 0$
$a + b \leq 0$
$a - b \geq 0$
$b - a \leq 0$
$a$ and $b$ must both be non-negative.
A student is testing points for the inequality $\frac{x}{3} - \frac{y}{2} > 1$. Which of their tests shows the correct work and conclusion?
Test point $(3, 2)$: $\frac{3}{3} - \frac{2}{2} = 1 - 1 = 0$. $0 > 1$ is false. So $(3,2)$ is not a solution.
Test point $(0, -2)$: $\frac{0}{3} - \frac{-2}{2} = 0 - (-1) = 1$. $1 > 1$ is false. So $(0,-2)$ is a solution.
Test point $(6, 0)$: $\frac{6}{3} - \frac{0}{2} = 2 - 0 = 2$. $2 > 1$ is true. So $(6,0)$ is not a solution.
Test point $(-3, -4)$: $\frac{-3}{3} - \frac{-4}{2} = -1 - (-2) = 1$. $1 > 1$ is false. So $(-3,-4)$ is a solution.
Test point $(9, 4)$: $\frac{9}{3} - \frac{4}{2} = 3 - 2 = 1$. The point is on the boundary line, so it is a solution.
Identify the linear inequation that represents the graph shown below.
$y < 2x - 1$
$y \leq 2x - 1$
$y > 2x - 1$
$y \geq 2x - 1$
$y > -2x - 1$
Which inequation corresponds to the graphical representation provided?
$2x + 5y \geq 10$
$2x + 5y > 10$
$2x + 5y \leq 10$
$2x + 5y < 10$
$5x + 2y \leq 10$
The graph shows a shaded region bounded by a vertical line. What is the inequation for this region?
$x < -2$
$x \leq -2$
$x > -2$
$y > -2$
$y < -2$
Determine the linear inequation that is represented by the given graph.
$y < 3$
$y > -1/3x$
$y \geq 3x$
$y \leq 1/3x$
$y = 3x+1$
Select the inequation that matches the graph. The line passes through the origin.
$2x + 3y \leq 0$
$2x + 3y \geq 0$
$3x + 2y \geq 0$
$3x - 2y \leq 0$
$y < -\frac{2}{3}x$
A graph of a linear inequation has a solid boundary line represented by the equation $y = x + 3$. The region below the line is shaded. Which of the following is the correct inequation?
$y < x + 3$
$y > x + 3$
$y \geq x + 3$
$y \leq x + 3$
$x \leq y - 3$
The boundary line of a linear inequation passes through the points $(4, 0)$ and $(0, -2)$. The line is dashed. The point $(1, 1)$ is a solution. Which inequation represents this information?
$x - 2y > 4$
$x - 2y < 4$
$x - 2y \geq 4$
$x - 2y \leq 4$
$x + 2y < 4$
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