2. Example 1: Equations with Variables on Each Side
Main Idea
Example 1: Equations with Variables on Each Side
Example 2: Equations with Variables on Each Side
Example 3: Real-World Example
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3. Solve equations with variables on each side.
Main Idea/Vocabulary

4. Equations with Variables on Each Side
Solve 7x + 4 = 9x. Check your solution.
7x + 4 = 9x Write the equation.
– 7x = – 7x Subtraction Property of Equality
4 = 2x Simplify by combining like terms.
Subtract 7x from the right side of the equation to keep it balanced.
Subtract 7x from the left side of the equation to isolate the variable.
Example 1

5. Equations with Variables on Each Side
Divide each side by 2.
2 = x Simplify.
Check To check your solution, replace x with 2 in the original equation.
7x + 4 = 9x Write the original equation.
7(2) + 4 = 9(2) Replace x with 2. ?
18 = 18 The sentence is true.
Answer: The solution is 2.
Example 1

6. Solve t = 12 – 2t. Check your solution.
A. t = 3
B. t = 4
C. t = 6
D. t = –12
Example 1 CYP

7. Equations with Variables on Each Side
Solve 3x – 2 = 8x + 13.
3x – 2 = 8x + 13 Write the equation.
– 3x = – 3x Subtraction Property of Equality
–2 = 5x + 13 Simplify.
– 13 = – 13 Subtraction Property of Equality
–15 = 5x Simplify.
–3 = x Mentally divide each side by 5.
Answer: x = –3
Example 2

8. Solve 4r – 6 = 7r + 3. A. r = 1 B. r = –1 C. r = 3 D. r = –3
Example 2 CYP

9. MEASUREMENT The measure of an angle is 8 degrees more than its complement. If x represents the measure of the angle and 90 – x represents the measure of its complement, what is the measure of the angle?
Example 3

10. x = 8 + (90 – x) Write the equation. x = 98 – x Simplify.
+ x = x Addition Property of Equality
2x = 98 Simplify.
x = 49 Simplify.
Division Property of Equality
Answer: The measure of the angle is 49°.
Example 3

11. MEASUREMENT The measure of an angle is 36 degrees less than its supplement. If x represents the measure of the angle and 180 – x represents the measure of its supplement, what is the measure of the angle?
A. 36°
B. 72°
C. 108°
D. 144°
Example 3 CYP