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Solve Multi-step Equations. 4x + 7 ( x – 2 ) = -8. 3 ( x – 4 ) = 6. Students will solve equations with multiple steps (more than two) using distributive property, combining like terms, and inverse operations. -3 = 3a + 5 ( a – 9 ) + 4. POWER to the brain. m – 9 – ( 3m + 4 ) = 1.

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## Solve Multi-step Equations

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**Solve Multi-step Equations**4x + 7 ( x – 2 ) = -8 3 ( x – 4 ) = 6 Students will solve equations with multiple steps (more than two) using distributive property, combining like terms, and inverse operations. -3 = 3a + 5 ( a – 9 ) + 4 POWER to the brain. m – 9 – ( 3m + 4 ) = 1**REVIEW: Simplify Using the Distributive Property.**Distributive Property – Multiply times everything in the parentheses. a ( b + c ) = ab – ac OR a ( b – c ) = ab + ac Example 1: -3 ( x + 5 ) -3x – 15 Example 2: -7 ( 2a – 4 ) + 28 -14a**REVIEW: Simplify Using Combining Like Terms**Like Terms must have the same variables and the same powers on the letters. Combine like terms by adding or subtracting the coefficients (numbers in front of the variables). Example 1: 3x + 5 – 7x + 9 + 14 -4x Example 2: 3 – 6y – 7 – 9y – 15y -4**How do we simplify and solve equations with multiple steps?**To solve equations with multiple steps, first use the distributive property to get rid of the parentheses. Then, combine like terms to get the problem in the 2-step form. Solve by using inverse operations as you do with 2-step equations.**Simplify and Solve**Example: 3x + 2 ( 2x – 1 ) = 33 • Use Distributive Property • 2. Combine Like terms • 3. Use Inverse Operations – 2 3x + = 33 4x – 2 = 33 7x + 2 + 2 7x = 35 7 7 x = 5**Now it’s a regular 2-step equation.**Simplify and Solve Equations FIRST - Use the Distributive Property to get rid of the parentheses. Example: 3 ( x – 2 ) + 4x = 8 – 6 + 4x = 8 3x SECOND: Combine like terms. Copy the rest of the problem. – 6 = 8 7x + 6 + 6 Add 6 to both sides. 7x = 14 Divide both sides by 7. 7 7 x = 2 Use your calculator for the computations if needed.**Simplify and SOLVE: -4y – 5 – 4( -2y – 3 ) + 8 = 3**Distributive Property - 4y – 5 + 8y + 8 = 3 +12 Combine like terms. Copy the rest of the problem. + 8 = 3 4y + 7 4y + 15 = 3 – 15 – 15 4y = -12 Use your calculator for the computations if needed. 4 4 y = -3**Simplify and Solve:**Distributive Property -5x + 3 – ( 9x – 2 ) + 7 = 96 – 9x -5x + 3 + 7 = 96 + 2 Combine Like Terms = 96 -14x + 12 – 12– 12 84 -14x = -14 -14 x = - 6 Use your calculator for the computations if needed.**SUMMARY**To solve equations with multiple steps, first use the distributive property to get rid of the parentheses. Then, combine like terms to get the problem in the 2-step form. Solve by using inverse operations as you do with 2-step equations.**Practice: Multi-step Equations 1**Copy the problems and solve for the variable. Be sure you show all your steps to receive full credit. NO WORK = NO CREDIT • 1. 2n + 3n + 7 = -41 • 2. 2x - 5x + 6.3 = -14.4 • 3. 2z + 9.75 - 7z = -5.15 • 4. 3h - 5h + 11 = 17 • 2t + 8 - t = -3 • 6. 6a - 2a = -36 • 7. 3c - 8c + 7 = -18 • 8. 7g + 14 - 5g = -8 • 9. 2b - 6 + 3b = 14 • 10. 2(a - 4) + 15 = 13 • 11. 7 + 2(a - 3) = -9 • 12. 13 + 2(5c - 2) = 29 • 13. 5(3x + 12) = -15 • 14. 4(2a + 2) - 17 = 15 • 15. 2(m + 1) = 16 16. -4x + 3(2x - 5) = 31 17. -6 - 3(2k + 4) = 18 18. 3(t - 12) = 27 19. -w + 4(w + 3) = -12 20. 4 = 0.4(3d - 5) 21. -4d + 2(3 + d) = -14 22. 2x + (4x + 16) = 7 23. 2(3a + 2) = -8 24. 5(t - 3) - 2t = -30 25. 5(b + 4) - 6b = -24 26. (5k + 35) - 8 = 12 27. 0.4(2s + 4) = 4.8 28. (9b - 27) = 36 29. (12n - 8) = 26 30. 0.5(2x - 4) = -17 STOP

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