# Solve Multi-step Equations (var. both sides) Students will solve multi-step equations with variables on both sides using distributive property, combining.

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Solve Multi-step Equations (var. both sides) Students will solve multi-step equations with variables on both sides using distributive property, combining like terms, and inverse operations. 3x + 2 ( x – 7 ) = 5 ( x – 9 ) + 11 -4y + 9 = -8 ( 2y – 3 ) -4m = -8m + 7m -9

To solve equations with variables on both sides… Simplify each side of the equation separately using Distributive Property and Combining Like Terms. Use Inverse Operations to move the term with the variable to the left side of the equation. Use Inverse Operations to solve the equations.

Solve: 5x + 3 = 2x + 15 –2x 3x + 3 = 15 – 3 3x = 12 3 x = 4 Check: 5(4) + 3 = 2(4) + 15 20 + 3 23 8 + 15 23 Use Inverse Operations to move the variable to the left side.

Simplify Each Side of the Equation and Solve x – 4 – 2 = 8 – ( 9 + x ) – 9 – x8 – x Distributive Property – 6 x C.L.T. x – 6 = = C.L.T. + x 2x Add x to both sides – 6 = -1 Add 6 to both sides + 6 2x = 5 Divide both sides by 2 2 2 Leave the answer as an improper fraction. Use Inverse Operations to move the variable to the left side.

Solve: -3x – x = -2x + 7 – 2x - 4x + 7 -4x = +4x = 7 0 ? 0 is NEVER equal to 7… That means “NO SOLUTION” Nothing will make the equation true.

Solve: 3 ( 2x – 5 ) = 6x – 15 6x– 15 = 6x – 15 −6x - 15 - 15 = If the numbers are equal, that means… “All Real Numbers” Any number will make the equation true.

Handout: Solve Multi-step Equations 1. Use distributive property and combine like terms to simplify each side of the equations separately. 2. Use inverse operation to move the variable to the front (left) side of the equation. 3. Solve the remaining equation by using inverse operations. STOP

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