Algebra Examples

Solve for x |2x-3|=9
|2x-3|=9|2x3|=9
Step 1
Remove the absolute value term. This creates a ±± on the right side of the equation because |x|=±x|x|=±x.
2x-3=±92x3=±9
Step 2
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.1
First, use the positive value of the ±± to find the first solution.
2x-3=92x3=9
Step 2.2
Move all terms not containing xx to the right side of the equation.
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Step 2.2.1
Add 33 to both sides of the equation.
2x=9+32x=9+3
Step 2.2.2
Add 99 and 33.
2x=122x=12
2x=122x=12
Step 2.3
Divide each term in 2x=122x=12 by 22 and simplify.
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Step 2.3.1
Divide each term in 2x=122x=12 by 22.
2x2=1222x2=122
Step 2.3.2
Simplify the left side.
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Step 2.3.2.1
Cancel the common factor of 22.
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Step 2.3.2.1.1
Cancel the common factor.
2x2=122
Step 2.3.2.1.2
Divide x by 1.
x=122
x=122
x=122
Step 2.3.3
Simplify the right side.
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Step 2.3.3.1
Divide 12 by 2.
x=6
x=6
x=6
Step 2.4
Next, use the negative value of the ± to find the second solution.
2x-3=-9
Step 2.5
Move all terms not containing x to the right side of the equation.
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Step 2.5.1
Add 3 to both sides of the equation.
2x=-9+3
Step 2.5.2
Add -9 and 3.
2x=-6
2x=-6
Step 2.6
Divide each term in 2x=-6 by 2 and simplify.
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Step 2.6.1
Divide each term in 2x=-6 by 2.
2x2=-62
Step 2.6.2
Simplify the left side.
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Step 2.6.2.1
Cancel the common factor of 2.
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Step 2.6.2.1.1
Cancel the common factor.
2x2=-62
Step 2.6.2.1.2
Divide x by 1.
x=-62
x=-62
x=-62
Step 2.6.3
Simplify the right side.
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Step 2.6.3.1
Divide -6 by 2.
x=-3
x=-3
x=-3
Step 2.7
The complete solution is the result of both the positive and negative portions of the solution.
x=6,-3
x=6,-3
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