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Solving Multi-Step Equations Define like terms again: Terms with exactly the same variables. Examples: Define the distributive property again: 6(3x + 2) Example:

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**Steps for Solving a Multi-Step Equation** Step 1 Clear the equation of fractions and decimals. Step 2 Use the Distributive Property to remove parentheses on each side. Step 3 Combine like terms on each side. Step 4 Undo addition or subtraction. Step 5 Undo multiplication or division.

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Solve 3a + 6 + a = 90 4a + 6=90Combine like terms. -6 -6 Subtract 6 from each side. 4a=84Simplify. 3a + 6 + a=90 Check: Solving Multi-Step Equations ALGEBRA 1 LESSON 2-3 2-3 =Divide each side by 4. a=21Simplify. 4a44a4 84 4

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You try: 3x – 4x + 6 = -2 3x + (-4x) + 6 = -2 - 1 x + 6 = -2 combined like terms -6 -6 subtract - 1x = -8 get rid of the negative variable x = 8 7 = 4m – 2m + 1 7 = 4m + (-2m) + 1 7 = 2m + 1 6 = 2m 2 m = 3 Don’t Forget: CHECK your solution

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Solve 2(x – 6) = 8 2x – 12=8Use the Distributive Property. +12 +12Add 6 to each side. 2x=20Simplify. x=10Simplify. Solving Multi-Step Equations ALGEBRA 1 LESSON 2-3 2-3 =Divide each side by 2. 2x22x2 20 2 2x + (-12) = 8

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You try: 3 ( k + 8 ) = 21 3k + 24 = 21 - 24 -24 3k = -3 3 3 k = -1 15 = -3(x – 1) + 9 15 = -3x – (-3) + 9 15 = -3x + 3 + 9 15 = -3x + 12 -12 3 = -3x -3 -1 = x

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You need to build a rectangular pen in your back yard for your dog. One side of the pen will be against the house. Two sides of the pen have a length of x ft and the width will be 25 ft. What is the greatest length the pen can be if you have 63 ft of fencing? Relate: length plus 25 ft plus length equals amount of side of side of fencing Define: Let x = length of a side adjacent to the house. Write: x + 25 + x = 63 Solving Multi-Step Equations ALGEBRA 1 LESSON 2-3 2-3

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x + 25 + x=63 The pen can be 19 ft long. 2x + 25=63Combine like terms. – 25= – 25Subtract 25 from each side. 2x=38Simplify. x=19 Solving Multi-Step Equations ALGEBRA 1 LESSON 2-3 2-3 (continued) =Divide each side by 2. 2x22x2 38 2

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Solve + = 17 3x23x2 x5x5 15x + 2x=170Multiply. 17x=170Combine like terms. x=10Simplify. Solving Multi-Step Equations ALGEBRA 1 LESSON 2-3 2-3 Method 2: Multiplying to clear fractions 10 ( + ) =10(17)Multiply each side by 10, a common multiple of 2 and 5. 3x23x2 x5x5 10 ( ) + 10 ( ) =10(17)Use the Distributive Property. 3x23x2 x5x5 =Divide each side by 17. 17x 17 170 17

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You try: 2 nd method: ¼ m + ½ m = 5/8 (8) ¼ m + (8) ½ m = 5/8 ( 8) 2m + 4m = 5 6m = 5 6 6 m = 5/6

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Solve 0.6a + 18.65 = 22.85. Solving Multi-Step Equations ALGEBRA 1 LESSON 2-3 2-3

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