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Warm Up

Warm Up. Solve and check: 7 x – 2 = 4 x 2) 7(5 x – 2) = 6(6 x – 1) 3) 3 x – 3 = 5( x – 4). 3 Points Total 1 for each. -5 -5. Use the multiplication property to “clear the equation” of fractions. The Fraction Buster Method. Example 1:.

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Warm Up

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

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

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

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

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