1. Linear Equations: Using the Properties Together
Section 2.2
Linear Equations: Using the Properties Together

2. Section 2.2 Objectives
1 Use the Addition and Multiplication Properties of Equality to Solve Linear Equations
2 Combine Like Terms and Use the Distributive Property to Solve Linear Equations
3 Solve a Linear Equation with the Variable on Both Sides of the Equation
4 Use Linear Equations to Solve Problems

3. Solving Linear Equations
Example:
Solve the linear equation 3x  9 = 24.
3x  9 = 24
3x  = 24 + 9
Add 9 to both sides of the equation.
3x = 15
Divide both sides of the equation by 3
x = 5
3(5)  9 = 24
Check your answer in the original equation.
15  9 = 24
24 = 24 

4. Solving by Combining Like Terms
Example:
Solve the equation 3x  8 = 2x  15
3x  8 = 2x  15
3x = 2x  7
Add 8 to both sides.
x =  7
Subtract 2x from both sides.
3(7)  8 = 2(7)  15
Check your answer in the original equation.
21  8 = 14  15
29 = 29 

5. Using the Distributive Property
Example:
Solve the equation 12  2x  3(x + 2) = 4x + 12 – x.
12  2x  3(x + 2) = 4x + 12 – x
12  2x  3x  6 = 4x + 12 – x
Use the Distributive Property.
6  5x = 3x + 12
Combine like terms.
6 = 8x + 12
Add 5x to both sides.
– 6 = 8x
Subtract 12 from both sides.
Divide both sides by 8 and simplify.
Be sure to check your answer.

6. Solving a Linear Equation
Step 1: Remove any parentheses using the Distributive Property.
Step 2: Combine like terms on each side of the equation.
Step 3: Use the Addition Property of Equality to get all variables on one side and all constants on the other side.
Step 4: Use the Multiplication Property of Equality to get the coefficient of the variable to equal 1.
Step 5: Check the solution to verify that it satisfies the original equation.

7. Solving Problems
A Chunky Cheeseburger contains 12 more grams of fat than a Happy Hamburger. Find the number of grams of fat in each sandwich if there are a total of 98 grams of fat in the two sandwiches by solving the equation x + (x + 12) = 98 where x represents the number of fat grams in a Happy Hamburger and x + 12 represents the number of fat grams in a Chunky Cheeseburger.
x + (x + 12) = 98
2x + 12 = 98
Simplify.
2x = 86
Subtract 12 from both sides.
x = 43
Divide both sides by 2.
There are 43 fat grams in a Happy Hamburger and = 55 fat grams in a Chunky Cheeseburger.