Mastering Linear Equations: A Comprehensive Guide to Unit 4 Homework 11
Welcome to Unit 4: Linear Equations! If you've found your way here, it's because you're ready to dive deeper into the world of linear equations and solve some challenging problems. This comprehensive guide will walk you through Homework 11, ensuring you understand and excel in each problem. Let's get started!
Understanding Linear Equations
Before we jump into the homework, let's quickly recap linear equations. A linear equation is a mathematical equation containing one or more variables, where the highest exponent of any variable is 1. In other words, it's a straight line on a graph. The general form of a linear equation is:
Ax + B = 0
where A and B are constants, and x is the variable.
Solving Linear Equations
To solve a linear equation, you need to isolate the variable. Here are the steps:
- Add or subtract the same number from both sides of the equation to eliminate the constant term.
- Divide or multiply both sides of the equation by the same non-zero number to make the coefficient of the variable 1.
- Check your solution by substituting it back into the original equation.
Homework 11: Problem 1
Solve for x: 3x - 5 = 14
Solution:
- Add 5 to both sides:
3x - 5 + 5 = 14 + 5 - Divide both sides by 3:
(3x - 5)/3 = 19/3 - Simplify:
x = 19/3
Homework 11: Problem 2
Solve for y: 4y + 3 = 13
Solution:
- Subtract 3 from both sides:
4y + 3 - 3 = 13 - 3 - Divide both sides by 4:
(4y + 3)/4 = 10/4 - Simplify:
y = 5/2
Homework 11: Problem 3
Solve for z: 2(z - 3) = 5
Solution:
- Divide both sides by 2:
(2(z - 3))/2 = 5/2 - Simplify the left side:
z - 3 = 5/2 - Add 3 to both sides:
z - 3 + 3 = 5/2 + 3 - Simplify:
z = 11/2
Practice Problems
Now that you've seen the solutions, try solving the following problems on your own:
- Solve for a:
7a + 2 = 23 - Solve for b:
3(b - 4) = 15 - Solve for c:
4(c + 2) - 3 = 11
Remember, the key to solving linear equations is to keep your equations balanced. Always do the same thing to both sides of the equation. Good luck!
