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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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**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

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**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

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**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.

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**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 7x = 35 x = 5

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**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. Add 6 to both sides. 7x = 14 Divide both sides by 7. x = 2 Use your calculator for the computations if needed.

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**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. y = -3

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**Distributive Property**

Simplify and Solve: Distributive Property -5x + 3 – ( 9x – 2 ) + 7 = 96 -5x = 96 – 9x + 2 Combine Like Terms -14x + 12 = 96 – – 12 -14x = 84 x = - 6 Use your calculator for the computations if needed.

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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.

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**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 = -14.4 3. 2z z = -5.15 4. 3h - 5h + 11 = 17 2t t = -3 6. 6a - 2a = -36 7. 3c - 8c + 7 = -18 8. 7g g = -8 9. 2b b = 14 (a - 4) + 15 = 13 (a - 3) = -9 (5c - 2) = 29 (3x + 12) = -15 (2a + 2) - 17 = 15 (m + 1) = 16 x + 3(2x - 5) = 31 (2k + 4) = 18 (t - 12) = 27 w + 4(w + 3) = -12 = 0.4(3d - 5) d + 2(3 + d) = -14 x + (4x + 16) = 7 (3a + 2) = -8 (t - 3) - 2t = -30 (b + 4) - 6b = -24 26. (5k + 35) - 8 = 12 (2s + 4) = 4.8 28. (9b - 27) = 36 29. (12n - 8) = 26 (2x - 4) = -17 STOP

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