Finite Math Examples

Solve for x |(7x-10)/8|=7x+1
Step 1
Remove the absolute value term. This creates a on the right side of the equation because .
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.
Step 2.2
Multiply both sides by .
Step 2.3
Simplify.
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Step 2.3.1
Simplify the left side.
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Step 2.3.1.1
Cancel the common factor of .
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Step 2.3.1.1.1
Cancel the common factor.
Step 2.3.1.1.2
Rewrite the expression.
Step 2.3.2
Simplify the right side.
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Step 2.3.2.1
Simplify .
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Step 2.3.2.1.1
Apply the distributive property.
Step 2.3.2.1.2
Multiply.
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Step 2.3.2.1.2.1
Multiply by .
Step 2.3.2.1.2.2
Multiply by .
Step 2.4
Solve for .
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Step 2.4.1
Move all terms containing to the left side of the equation.
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Step 2.4.1.1
Subtract from both sides of the equation.
Step 2.4.1.2
Subtract from .
Step 2.4.2
Move all terms not containing to the right side of the equation.
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Step 2.4.2.1
Add to both sides of the equation.
Step 2.4.2.2
Add and .
Step 2.4.3
Divide each term in by and simplify.
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Step 2.4.3.1
Divide each term in by .
Step 2.4.3.2
Simplify the left side.
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Step 2.4.3.2.1
Cancel the common factor of .
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Step 2.4.3.2.1.1
Cancel the common factor.
Step 2.4.3.2.1.2
Divide by .
Step 2.4.3.3
Simplify the right side.
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Step 2.4.3.3.1
Move the negative in front of the fraction.
Step 2.5
Next, use the negative value of the to find the second solution.
Step 2.6
Multiply both sides by .
Step 2.7
Simplify.
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Step 2.7.1
Simplify the left side.
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Step 2.7.1.1
Cancel the common factor of .
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Step 2.7.1.1.1
Cancel the common factor.
Step 2.7.1.1.2
Rewrite the expression.
Step 2.7.2
Simplify the right side.
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Step 2.7.2.1
Simplify .
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Step 2.7.2.1.1
Apply the distributive property.
Step 2.7.2.1.2
Multiply.
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Step 2.7.2.1.2.1
Multiply by .
Step 2.7.2.1.2.2
Multiply by .
Step 2.7.2.1.3
Apply the distributive property.
Step 2.7.2.1.4
Multiply.
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Step 2.7.2.1.4.1
Multiply by .
Step 2.7.2.1.4.2
Multiply by .
Step 2.8
Solve for .
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Step 2.8.1
Move all terms containing to the left side of the equation.
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Step 2.8.1.1
Add to both sides of the equation.
Step 2.8.1.2
Add and .
Step 2.8.2
Move all terms not containing to the right side of the equation.
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Step 2.8.2.1
Add to both sides of the equation.
Step 2.8.2.2
Add and .
Step 2.8.3
Divide each term in by and simplify.
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Step 2.8.3.1
Divide each term in by .
Step 2.8.3.2
Simplify the left side.
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Step 2.8.3.2.1
Cancel the common factor of .
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Step 2.8.3.2.1.1
Cancel the common factor.
Step 2.8.3.2.1.2
Divide by .
Step 2.9
The complete solution is the result of both the positive and negative portions of the solution.
Step 3
Exclude the solutions that do not make true.
Step 4
The result can be shown in multiple forms.
Exact Form:
Decimal Form: