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**Solve equations with variables on each side.**

Main Idea/Vocabulary

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**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

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**Solve 3x + 6 = x. Check your solution.**

A. –5 B. –3 C. –1 D. 1 A B C D Example 1

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**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

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**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

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

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**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

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**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

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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

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(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

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(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

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(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

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(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

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(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

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**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

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Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

Solve an equation using subtraction EXAMPLE 1 Solve x + 7 = 4. x + 7 = 4x + 7 = 4 Write original equation. x + 7 – 7 = 4 – 7 Use subtraction property of.

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