 # 1 Warm Up 3 Points Total 1 for each Solve and check: 7x – 2 = 4x 2) 7(5x – 2) = 6(6x – 1) 3) 3x – 3 = 5(x – 4)

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1 Warm Up 3 Points Total 1 for each Solve and check: 7x – 2 = 4x 2) 7(5x – 2) = 6(6x – 1) 3) 3x – 3 = 5(x – 4)

2 The Fraction Buster Method Example 1: Use the multiplication property to “clear the equation” of fractions. 4x + 3x = 5 + 12x 7x = 5 + 12x -12x -5x = 5 -5 -5 Yuk! What’s the Least Common Denominator? Now distribute the 6 and simplify. x = -1 Substitution will show that –1 checks.

3 The Fraction Buster Method Can you find a multiplier that will simplify the equations? Multiply by 12, the LCD. Now, you try it. Find a multiplier, simplify and solve this equation. Don’t forget to check! Multiply by 3. p = 4 2x – 1 = 5x + 7 9x – 84 = 96 + 8x

4 Equations With Decimals Example 2: Use the multiplication property to “clear the equation” of decimals, by multiplying the equation by a power of 10. 100(0.21x + 4.52) = 100(-0.73 – 0.84x) 21x + 452 = -73 – 84x -21x +73 +73 -21x 525 = -105x Yuk! But what if I multiply the equation by 100? 0.21x + 4.52 = -0.73 – 0.84x x = -5 Substitution will show that -5 checks.

5 Equations with Decimals Can you find a multiplier that will simplify the equations? Multiply by 100. Now, you try it. Find a multiplier, simplify and solve this equation. Don’t forget to check! Multiply by 10. y = 3 0.5r + 1.5 = 3.0 5r + 15 = 30 16.3 – 7.2y = -8.18 1630 – 720y = -818 0.42 – 0.03y = 3.33 – y

6 Summary of Methods for Solving Equations If necessary, multiply both sides of the equation by a power of 10 to clear decimals. Or, if necessary, multiply both sides of the equation by a common denominator to clear fractions. Use the distributive property to simplify and to remove parentheses. Collect like terms on each side, if necessary. Use the addition property to move the variable to one side and all other terms to the other side of the equation. Collect like terms again, if necessary. Use the multiplication property to solve for the variable.

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