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11-2 Solving Multi-Step Equations Warm Up Solve. 1. 3x = 102 x = 34 2. y = 15 y = 225 15 3. z – 100 = 21 z = 121 4. 1.1 + 5w = 98.6 w = 19.5 11-2 Solving Multi-Step Equations Learn to solve multi-step equations. 11-2 Solving Multi-Step Equations To solve a multi-step equation, you may have to simplify the equation first by combining like terms or by using the Distributive Property. 11-2 Solving Multi-Step Equations Additional Example 1A: Solving Equations That Contain Like Terms Solve. 8x + 6 + 3x – 2 = 37 11x + 4 = 37 –4 –4 11x = 33 11x = 33 11 11 x=3 Combine like terms. Subtract 4 from both sides. Divide both sides by 11. 11-2 Solving Multi-Step Equations Additional Example 1B: Solving Equations That Contain Like Terms Solve. 4(x – 6) + 7 = 11 4(x – 6) + 7 = 11 Distributive Property 4(x) – 4(6) + 7 = 11 Simplify by multiplying: 4x – 24 + 7 = 11 4(x) = 4x and 4(6) = 24. 4x – 17 = 11 Simplify by adding: –24 + 7 = 17. + 17 +17 Add 17 to both sides. 4x = 28 4 4 Divide both sides by 4. x=7 11-2 Solving Multi-Step Equations Check It Out: Example 1 Solve. 9x + 5 + 4x – 2 = 42 13x + 3 = 42 Combine like terms. – 3 – 3 Subtract 3 from both sides. 13x = 39 13x = 39 Divide both sides by 13. 13 13 x=3 11-2 Solving Multi-Step Equations Remember! The least common denominator (LCD) is the smallest number that each of the denominators will divide into. 11-2 Solving Multi-Step Equations Additional Example 2: Solving Equations That Contain Fractions Solve. 7x + x – 17 = 2 3 2 9 9 The LCD is 18. Multiply both 17 7x x 2 18 + – 9 = 18 sides by 18. 9 2 3 7x x 17 2 Distributive 18 9 + 18 2 – 18 9 = 18 3 Property. () ( () ) () () () 14x + 9x – 34 = 12 23x – 34 = 12 Combine like terms. 11-2 Solving Multi-Step Equations Additional Example 2 Continued 23x – 34 = 12 Combine like terms. + 34 + 34 23x = 46 23x = 46 23 23 Add 34 to both sides. x=2 Divide both sides by 23.