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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)
17z
8x
3
2x
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 -12x
-5x = 5 -5 -5
xxx 26
5
2
1
3
2
Yuk! What’s the Least Common Denominator?
xxx 2
6
56
2
1
3
26 Now distribute the 6
and simplify.
x = -1
Substitution will show that –1 checks.
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The Fraction Buster MethodCan you find a multiplier that will simplify the equations?
2
3
6
1
3
1p
3
7
3
5
3
1
3
2 xx
Multiply by 12, the LCD.
Now, you try it. Find a multiplier, simplify and solve this equation.
Don’t forget to check!
xx3
287
4
3
Multiply by 3.
p = 4
2x – 1 = 5x + 7
9x – 84 = 96 + 8x
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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.
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Equations with DecimalsCan 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 = 3.05r + 15 = 30
16.3 – 7.2y = -8.18
1630 – 720y = -818
0.42 – 0.03y = 3.33 – y
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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.
