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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
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

the fraction buster method

-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

the fraction buster method1

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

equations with decimals

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

equations with decimals1

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

summary of methods for solving equations
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.