Algebra Examples

Solve for x -1/2|x-5|+3=2
Step 1
Combine and .
Step 2
Move all terms not containing to the right side of the equation.
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Step 2.1
Subtract from both sides of the equation.
Step 2.2
Subtract from .
Step 3
Multiply both sides of the equation by .
Step 4
Simplify both sides of the equation.
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Step 4.1
Simplify the left side.
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Step 4.1.1
Simplify .
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Step 4.1.1.1
Cancel the common factor of .
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Step 4.1.1.1.1
Move the leading negative in into the numerator.
Step 4.1.1.1.2
Factor out of .
Step 4.1.1.1.3
Cancel the common factor.
Step 4.1.1.1.4
Rewrite the expression.
Step 4.1.1.2
Multiply.
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Step 4.1.1.2.1
Multiply by .
Step 4.1.1.2.2
Multiply by .
Step 4.2
Simplify the right side.
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Step 4.2.1
Multiply by .
Step 5
Remove the absolute value term. This creates a on the right side of the equation because .
Step 6
The complete solution is the result of both the positive and negative portions of the solution.
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Step 6.1
First, use the positive value of the to find the first solution.
Step 6.2
Move all terms not containing to the right side of the equation.
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Step 6.2.1
Add to both sides of the equation.
Step 6.2.2
Add and .
Step 6.3
Next, use the negative value of the to find the second solution.
Step 6.4
Move all terms not containing to the right side of the equation.
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Step 6.4.1
Add to both sides of the equation.
Step 6.4.2
Add and .
Step 6.5
The complete solution is the result of both the positive and negative portions of the solution.