1. Solve equations with variables on each side.
Main Idea/Vocabulary

2. Equations with Variables on Each Side
Solve 7x + 4 = 9x. Check your solution.
Write the equation.
Subtract 7x from each side.
Simplify by combining like terms.
Mentally divide each side by 2.
To check your solution, replace x with 2 in the original equation.
Check
Write the equation. ?
Replace x with 2. 
The sentence is true.
Answer: The solution is 2.
Example 1

3. Solve 3x + 6 = x. Check your solution.
A. –5
B. –3
C. –1
D. 1 A B C D
Example 1

4. Equations with Variables on Each Side
Solve 3x – 2 = 8x Check your solution.
Write the equation.
Subtract 8x from each side.
Simplify.
Add 2 to each side.
Simplify.
Mentally divide each side by –5.
To check your solution, replace x with –3 in the original equation.
Example 2

5. Equations with Variables on Each Side
Check
3x – 2 = 8x + 13 Write the equation.
3(–3) – 2 = 8(–3) + 13 Replace x with –3.
– 11 = –11 The sentence is true. 
Answer: The solution is –3.
Example 2

6. Solve 4x – 3 = 5x + 7.
A. –4
B. –7
C. –10
D. –12 A B C D
Example 2

7. Variable Let x and 90 – x represent the measure of the angles.
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?
Words The measure of an angle equals the measure of its complement plus 8.
Variable Let x and 90 – x represent the measure of the angles.
Equation x = 90 – x + 8
Example 3

8. x = 90 – x + 8 Write the equation. x = 98 – x Simplify.
x + x = 98 – x + x Add x to each side.
2x = 98
Divide each side by 2.
x = 49
Answer: The measure of the angle is 49 degrees.
Example 3

9. MEASUREMENT The measure of an angle is 12 degrees less 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?
A. 39 degrees
B. 42 degrees
C. 47 degrees
D. 51 degrees A B C D
Example 3

10. (over Lesson 8-3)
Translate the sentence into an equation. Then find the number. The difference of three times a number and 5 is 10.
A. 3 – n = 10; 7
B. 3 – n = 10; –7
C. 3n – 5 = 10; –5
D. 3n – 5 = 10; 5 A B C D
Five Minute Check 1

11. (over Lesson 8-3)
Translate the sentence into an equation. Then find the number. Three more than four times a number equals 27.
A. 4n + 3 = 27; 6
B. 3 – 4n = 27; –6 C. D. A B C D
Five Minute Check 2

12. (over Lesson 8-3)
Translate the sentence into an equation. Then find the number. Nine more than seven times a number is 58. A.
B. 7n + 9 = 58; 7 C. D. A B C D
Five Minute Check 3

13. (over Lesson 8-3)
Translate the sentence into an equation. Then find the number. Four less than the quotient of a number and three equals 14. A. B. C. D. A B C D
Five Minute Check 4

14. (over Lesson 8-3)
Jared went to a photographer and purchased one 8 x 10 portrait. He also purchased 20 wallet-sized pictures. Jared spent $97 in all, and the 8 x 10 cost $33. How much is each of the wallet-sized photos?
A. $2.33
B. $3.20
C. $3.61
D. $6.50 A B C D
Five Minute Check 5

15. What is the value of x in the trapezoid?
(over Lesson 8-3)
What is the value of x in the trapezoid?
A. 35
B. 55
C. 70
D. 105 A B C D
Five Minute Check 6

16. End of Custom Shows