Basic Math Examples

Solve for a |4a+6|-4a=-10
Step 1
Add to both sides of the equation.
Step 2
Remove the absolute value term. This creates a on the right side of the equation because .
Step 3
The complete solution is the result of both the positive and negative portions of the solution.
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Step 3.1
First, use the positive value of the to find the first solution.
Step 3.2
Move all terms containing to the left side of the equation.
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Step 3.2.1
Subtract from both sides of the equation.
Step 3.2.2
Combine the opposite terms in .
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Step 3.2.2.1
Subtract from .
Step 3.2.2.2
Add and .
Step 3.3
Since , there are no solutions.
No solution
Step 3.4
Next, use the negative value of the to find the second solution.
Step 3.5
Simplify .
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Step 3.5.1
Rewrite.
Step 3.5.2
Simplify by adding zeros.
Step 3.5.3
Apply the distributive property.
Step 3.5.4
Multiply.
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Step 3.5.4.1
Multiply by .
Step 3.5.4.2
Multiply by .
Step 3.6
Move all terms containing to the left side of the equation.
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Step 3.6.1
Add to both sides of the equation.
Step 3.6.2
Add and .
Step 3.7
Move all terms not containing to the right side of the equation.
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Step 3.7.1
Subtract from both sides of the equation.
Step 3.7.2
Subtract from .
Step 3.8
Divide each term in by and simplify.
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Step 3.8.1
Divide each term in by .
Step 3.8.2
Simplify the left side.
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Step 3.8.2.1
Cancel the common factor of .
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Step 3.8.2.1.1
Cancel the common factor.
Step 3.8.2.1.2
Divide by .
Step 3.8.3
Simplify the right side.
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Step 3.8.3.1
Cancel the common factor of and .
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Step 3.8.3.1.1
Factor out of .
Step 3.8.3.1.2
Cancel the common factors.
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Step 3.8.3.1.2.1
Factor out of .
Step 3.8.3.1.2.2
Cancel the common factor.
Step 3.8.3.1.2.3
Rewrite the expression.
Step 3.9
The complete solution is the result of both the positive and negative portions of the solution.