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# Learn to solve multi-step equations .

Learn to solve multi-step equations . To solve a multi-step equation, you may have to simplify the equation first by combining like terms or by using the Distributive Property. 33. 11 x. =. 11. 11. Additional Example 1A: Solving Equations That Contain Like Terms. Solve.

## Learn to solve multi-step equations .

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1. Learn to solve multi-step equations.

2. To solve a multi-step equation, you may have to simplify the equation first by combining like terms or by using the Distributive Property.

3. 33 11x = 11 11 Additional Example 1A: Solving Equations That Contain Like Terms Solve. 8x + 6 + 3x – 2 = 37 11x + 4 = 37 Combine like terms. – 4– 4Subtract 4 from both sides. 11x = 33 Divide both sides by 11. x = 3

4. ? 8(3) + 6 + 3(3) – 2 = 37 ? 24 + 6 + 9 – 2 = 37 ? 37 = 37 Additional Example 1A Continued Check 8x + 6 + 3x – 2 = 37 Substitute 3 for x. 

5. 4 4 Additional Example 1B: Solving Equations That Contain Like Terms Solve. 4(x – 6) + 7 = 11 4(x – 6) + 7 = 11Distributive Property 4(x)– 4(6) + 7 = 11 Simplify by multiplying: 4(x) = 4x and 4(6) = 24. 4x – 24 + 7 = 11 4x – 17 = 11 Simplify by adding: –24 + 7 = 17. + 17+17Add 17 to both sides. 4x = 28 Divide both sides by 4. x = 7

6. 39 13x = 13 13 Check It Out: Example 1 Solve. 9x + 5 + 4x – 2 = 42 13x + 3 = 42 Combine like terms. – 3– 3Subtract 3 from both sides. 13x = 39 Divide both sides by 13. x = 3

7. ? 9(3) + 5 + 4(3) – 2 = 42 ? 27 + 5 + 12 – 2 = 42 ? 42 = 42 Check It Out: Example 1 Continued Check 9x + 5 + 4x – 2 = 42 Substitute 3 for x. 

8. If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) of the fractions. This step results in an equation without fractions, which may be easier to solve.

9. Remember! The least common denominator (LCD) is the smallest number that each of the denominators will divide into.

10. x 7x 2 9 17 x 17 2 2 18+ – = 18 2 9 ( ) () 3 9 3 x 7x 2 9 7x 9 18( ) + 18( ) – 18( ) = 18( ) 2 17 3 9 Additional Example 2: Solving Equations That Contain Fractions Solve. + – = The LCD is 18. Multiply both sides by 18. Distributive Property. 14x + 9x – 34 = 12 23x – 34 = 12 Combine like terms.

11. 46 = Divide both sides by 23. 23 23x 23 Additional Example 2 Continued 23x – 34 = 12 Combine like terms. + 34+ 34Add 34 to both sides. 23x = 46 x = 2

12. x 7x 2 9 (2) ? + – = Substitute 2 for x. 2 17 17 6 17 2 17 2 2 2 2 9 17 9 9 9 3 9 3 9 9 3 3 9 2 ? ? ? 14 14 7(2) 14 + – = + – = + – = 9 9 9 9 1 ? = 6 6 9 9 The LCD is 9. Additional Example 2 Continued Check + – = 

13. 5 5 5 –1 1 –1 4 4 4 4 4 4 3n 3n 3n ( )( ) 4 4 4 4 + = 4 ( )( )( ) 4 + 4 = 4 Check It Out: Example 2A Solve. + = – Multiply both sides by 4 to clear fractions, and then solve. Distributive Property. 3n + 5 = –1

14. –6 Divide both sides by 3. 3 3n = 3 Check It Out: Example 2A Continued 3n + 5 = –1 – 5–5Subtract 5 from both sides. 3n = –6 n = –2

15. x 5x 3 9 13 x 13 1 1 9+ – = 9( ) 3 9 ( ) 3 9 3 x 5x 3 9 5x 9( ) + 9( )– 9( ) = 9( ) 9 1 13 3 9 Check It Out: Example 2B Solve. + – = The LCD is 9. Multiply both sides by 9. Distributive Property. 5x + 3x – 13 = 3 8x – 13 = 3 Combine like terms.

16. 16 = Divide both sides by 8. 8 8x 8 Check It Out: Example 2B Continued 8x – 13 = 3 Combine like terms. + 13+ 13Add 13 to both sides. 8x = 16 x = 2

17. x 5x 3 9 (2) ? + – = Substitute 2 for x. 3 6 13 3 13 2 13 1 1 13 1 9 3 3 9 9 9 3 9 3 9 ? ? 10 10 5(2) + – = + – = 9 9 9 ? = 3 3 9 9 The LCD is 9. Check It Out: Example 2B Continued Check + – = 

18. 9 16 25 2x 5 x 6x 33 8 8 8 7 21 21 x = 1 Lesson Quiz Solve. 1. 6x + 3x – x + 9 = 33 2. 8(x + 2) + 5 = 29 3. + = 5. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned \$544. What is her hourly rate? x = 3 x = 1 x = 28 4. – = \$8.50

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