Solve Multi-step Equations LESSON 6.2.2 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 ) -14a + 28

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 -4x + 14 Example 2: 3 – 6y – 7 – 9y -4 – 15y

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 3x + = 33 4x – 2 7x – 2 = 33 + 2 + 2 7x = 35 7 7 x = 5

Simplify and Solve Equations FIRST - Use the Distributive Property to get rid of the parentheses. Example: 3 ( x – 2 ) + 4x = 8 SECOND: Combine like terms. 3x – 6 + 4x = 8 Copy the rest of the problem. 7x – 6 = 8 Now it’s a regular 2-step equation. + 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 + 12 + 8 = 3 Copy the rest of the problem. Combine like terms. 4y + 7 + 8 = 3 4y + 15 = 3 – 15 – 15 4y = -12 Use your calculator for the computations if needed. 4 4 y = -3

Distributive Property Simplify and Solve: Distributive Property -5x + 3 – ( 9x – 2 ) + 7 = 96 -5x + 3 + 7 = 96 – 9x + 2 Combine Like Terms -14x + 12 = 96 – 12 – 12 -14x = 84 -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