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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.

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## Learn to solve multi-step equations .

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**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**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**?**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. **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**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**?**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. **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.**Remember!**The least common denominator (LCD) is the smallest number that each of the denominators will divide into.**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.**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**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 + – = **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**–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**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**= 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**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 + – = **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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