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Pre-Algebra Solving Equations with Variables on Both Sides 7-5 Objectives: 1. 2. OBJECTIVE 1 Collecting the Variable on One Side STEPS FOR SOLVING MULTI-STEP EQUATIONS EXAMPLE 1 Step 1 Use the Distributive Property. Step 2 Combine like terms on each side. Step 3 Move the variables to one side of the equation. Step 4 Undo addition or subtraction. Step 5 Undo multiplication or division. Collecting the Variable on One Side Solve each equation. 1. 9x + 2 = 4x – 18 STEPS 1. Subtract 4x from each side. 2. Simplify. 3. Subtract 2 from each side. 4. Simplify. 5. Divide each side by 5. 6. Simplify. 2. 4x + 4 = 2x + 36 3. -15 + 6b = -8b + 13 4. 4c + 3 = 15 – 2c OBJECTIVE 2 EXAMPLE 1 Using Equations With Variables on Both Sides Using the Distributive Property and Combine Like Terms First Solve each equation. 1. -2(y + 6) = y + 3 + 2y STEPS 1. Distribute the -2. 2. Combine Like Terms. 3. Subtract 3y from both sides. 4. Simplify 5. Add 12 to both sides. 6. Simplify 7. Divide both sides by -5. 8. Simplify. 1. 6(g + 3) = -2(g + 31) 2. 7a – 4 + 2a = 3a - 2 3. 7x + 9 = 4x 4. 8m – 5 = 5m + 7 5. x + 7x + 15x = 29x + 18 6. 8(7 – p) – 8 = -16(p – 2) 7. k + k + k = k + 18 8. 3(n – 5) = -2n 9. 4(y – 9) = 3(2y – 8) 10. 6(z – 2) + 3 = 3z – 15 11. -2x + 7 = x – 8 12. 7(v – 4) = 3(3 + v) – 1 Pre-Algebra Objectives 7.5 The student should be able…. 1. To solve equations with variables on both sides. 2. To use equations with variables on both sides.