1. Ch 2.4 (part 2) Multi-Step Objective: To solve multi-step variable equations by using three or more properties.

2. Definition Multi-Step Equation Three (or more) operations are performed:  Distributive Property  Combining LIKE Terms  Inverse Property of Addition  Inverse Property of Multiplication Distribute first - then perform the operations in REVERSE ORDER from the Order of Operations

3. GOAL: Isolate the variable expression then Isolate the variable 1) Use the Distributive Property. (then simplify by combining LIKE Terms) 2) Use Inverse Property of Addition. (Undo addition with subtraction. Undo subtraction with addition.) 3) Use Inverse Property of Multiplication. (Hint: Multiply by the reciprocal for fractions) Perform Inverse operations to both sides of the equation! Rules

4. 8 = 5(x - 4) + 2x 8 = 5x – 20 + 2x 8 = 7x - 20 +20 28 = 7x 7 Example 1  Distributive Property  Combine LIKE Terms  Inverse Property of Addition  Inverse Property of Multiplication

5. 4(x + 6) = 12 5(b + 5) = -5 4x + 24 = 12 -24 4x = -12 4 5b + 25 = -5 -25 5b = -30 5 5 b = -6 Example 2 Example 3 x = -3

6. (-1) 1) 3(x - 2) = 17 3) 12 - 2(x + 4) = 28 2) -(5 - x) = 94) 3x - 6 = 17 +6 3x = 23 3 -5 + x = 9 +5 x = 14 12 - 2x - 8 = 28 -2x + 4 = 28 -4 -2x = 24 -2 x = -12 (4) 5 - y = 40 -5 -y = 35(-1) y = -35 Solve.

7. 5) 6(x + 4) - 2(x - 7) = 10 6x + 24 - 2x + 14 = 10 4x + 38 = 10 -38 4x = -28 4 x = -7 Solve.

8. 6) 8 - 4[x - (2x + 4)] = 16 8 - 4[x - 2x - 4] = 16 8 - 4[-x - 4] = 16 8 + 4x + 16 = 16 4x + 24 = 16 -24 4x = -8 4 x = -2 Solve.