Transcript Properties of Tangents

Solve and check:
• 7x – 2 = 4x
2
x
3
Warm Up
2) 7(5x – 2) = 6(6x – 1)
x  8
3) 3x – 3 = 5(x – 4)
z  17
3 Points Total
1 for each
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The Fraction Buster Method
Use the multiplication property to “clear the equation” of fractions.
Example 1:
Yuk! What’s the Least
2
1
5
Common Denominator?
x  x   2x
3
2
6
1  5
2

Now distribute the 6
6 x  x   6  2 x 
2  6
3
 and simplify.
4x + 3x = 5 + 12x
7x = 5 + 12x
-12x
-12x
-5x = 5
Substitution will show that –1
-5 -5
checks.
x = -1
2
The Fraction Buster Method
Can you find a multiplier that will simplify the equations?
2
1 5
7
x  x
3
3 3
3
Multiply by 3.
2x – 1 = 5x + 7
3
2
x7  8 x
4
3
9x – 84 = 96 + 8x
Multiply by 12, the
LCD.
Now, you try it. Find a multiplier, simplify and solve this equation.
Don’t forget to check!
1
1 3
p 
3
6 2
p=4
3
Equations With Decimals
Use the multiplication property to “clear the equation” of decimals,
by multiplying the equation by a power of 10.
Example 2:
0.21x + 4.52 = -0.73 – 0.84x
Yuk! But what if I
multiply the equation by 100?
100(0.21x + 4.52) = 100(-0.73 – 0.84x)
21x + 452 = -73 – 84x
-21x +73 +73 -21x
525 = -105x
x = -5
Substitution will show that -5 checks.
4
Equations with Decimals
Can you find a multiplier that will simplify the equations?
0.5r + 1.5 = 3.0
5r + 15 = 30
Multiply by 10.
16.3 – 7.2y = -8.18
1630 – 720y = -818
Multiply by 100.
Now, you try it. Find a multiplier, simplify and solve this equation.
Don’t forget to check!
0.42 – 0.03y = 3.33 – y
y=3
5
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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