Basic Math Examples

Solve for a |1/2a+1/12|=|1/8a+1/3|
Step 1
Rewrite the equation as .
Step 2
Rewrite the absolute value equation as four equations without absolute value bars.
Step 3
After simplifying, there are only two unique equations to be solved.
Step 4
Solve for .
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Step 4.1
Combine and .
Step 4.2
Combine and .
Step 4.3
Move all terms containing to the left side of the equation.
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Step 4.3.1
Subtract from both sides of the equation.
Step 4.3.2
To write as a fraction with a common denominator, multiply by .
Step 4.3.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.3.3.1
Multiply by .
Step 4.3.3.2
Multiply by .
Step 4.3.4
Combine the numerators over the common denominator.
Step 4.3.5
Simplify each term.
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Step 4.3.5.1
Simplify the numerator.
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Step 4.3.5.1.1
Factor out of .
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Step 4.3.5.1.1.1
Raise to the power of .
Step 4.3.5.1.1.2
Factor out of .
Step 4.3.5.1.1.3
Factor out of .
Step 4.3.5.1.1.4
Factor out of .
Step 4.3.5.1.2
Multiply by .
Step 4.3.5.1.3
Subtract from .
Step 4.3.5.2
Move to the left of .
Step 4.3.5.3
Move the negative in front of the fraction.
Step 4.4
Move all terms not containing to the right side of the equation.
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Step 4.4.1
Subtract from both sides of the equation.
Step 4.4.2
To write as a fraction with a common denominator, multiply by .
Step 4.4.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 4.4.3.1
Multiply by .
Step 4.4.3.2
Multiply by .
Step 4.4.4
Combine the numerators over the common denominator.
Step 4.4.5
Subtract from .
Step 4.4.6
Cancel the common factor of and .
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Step 4.4.6.1
Factor out of .
Step 4.4.6.2
Cancel the common factors.
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Step 4.4.6.2.1
Factor out of .
Step 4.4.6.2.2
Cancel the common factor.
Step 4.4.6.2.3
Rewrite the expression.
Step 4.4.7
Move the negative in front of the fraction.
Step 4.5
Multiply both sides of the equation by .
Step 4.6
Simplify both sides of the equation.
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Step 4.6.1
Simplify the left side.
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Step 4.6.1.1
Simplify .
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Step 4.6.1.1.1
Cancel the common factor of .
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Step 4.6.1.1.1.1
Move the leading negative in into the numerator.
Step 4.6.1.1.1.2
Move the leading negative in into the numerator.
Step 4.6.1.1.1.3
Factor out of .
Step 4.6.1.1.1.4
Cancel the common factor.
Step 4.6.1.1.1.5
Rewrite the expression.
Step 4.6.1.1.2
Cancel the common factor of .
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Step 4.6.1.1.2.1
Factor out of .
Step 4.6.1.1.2.2
Cancel the common factor.
Step 4.6.1.1.2.3
Rewrite the expression.
Step 4.6.1.1.3
Multiply.
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Step 4.6.1.1.3.1
Multiply by .
Step 4.6.1.1.3.2
Multiply by .
Step 4.6.2
Simplify the right side.
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Step 4.6.2.1
Simplify .
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Step 4.6.2.1.1
Cancel the common factor of .
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Step 4.6.2.1.1.1
Move the leading negative in into the numerator.
Step 4.6.2.1.1.2
Move the leading negative in into the numerator.
Step 4.6.2.1.1.3
Factor out of .
Step 4.6.2.1.1.4
Cancel the common factor.
Step 4.6.2.1.1.5
Rewrite the expression.
Step 4.6.2.1.2
Combine and .
Step 4.6.2.1.3
Multiply by .
Step 5
Solve for .
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Step 5.1
Combine and .
Step 5.2
Simplify .
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Step 5.2.1
Combine and .
Step 5.2.2
Apply the distributive property.
Step 5.3
Move all terms containing to the left side of the equation.
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Step 5.3.1
Add to both sides of the equation.
Step 5.3.2
To write as a fraction with a common denominator, multiply by .
Step 5.3.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 5.3.3.1
Multiply by .
Step 5.3.3.2
Multiply by .
Step 5.3.4
Combine the numerators over the common denominator.
Step 5.3.5
Add and .
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Step 5.3.5.1
Reorder and .
Step 5.3.5.2
Add and .
Step 5.4
Move all terms not containing to the right side of the equation.
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Step 5.4.1
Subtract from both sides of the equation.
Step 5.4.2
To write as a fraction with a common denominator, multiply by .
Step 5.4.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 5.4.3.1
Multiply by .
Step 5.4.3.2
Multiply by .
Step 5.4.4
Combine the numerators over the common denominator.
Step 5.4.5
Subtract from .
Step 5.4.6
Move the negative in front of the fraction.
Step 5.5
Multiply both sides of the equation by .
Step 5.6
Simplify both sides of the equation.
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Step 5.6.1
Simplify the left side.
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Step 5.6.1.1
Simplify .
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Step 5.6.1.1.1
Cancel the common factor of .
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Step 5.6.1.1.1.1
Cancel the common factor.
Step 5.6.1.1.1.2
Rewrite the expression.
Step 5.6.1.1.2
Cancel the common factor of .
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Step 5.6.1.1.2.1
Factor out of .
Step 5.6.1.1.2.2
Cancel the common factor.
Step 5.6.1.1.2.3
Rewrite the expression.
Step 5.6.2
Simplify the right side.
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Step 5.6.2.1
Simplify .
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Step 5.6.2.1.1
Cancel the common factor of .
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Step 5.6.2.1.1.1
Move the leading negative in into the numerator.
Step 5.6.2.1.1.2
Factor out of .
Step 5.6.2.1.1.3
Factor out of .
Step 5.6.2.1.1.4
Cancel the common factor.
Step 5.6.2.1.1.5
Rewrite the expression.
Step 5.6.2.1.2
Cancel the common factor of .
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Step 5.6.2.1.2.1
Factor out of .
Step 5.6.2.1.2.2
Cancel the common factor.
Step 5.6.2.1.2.3
Rewrite the expression.
Step 5.6.2.1.3
Combine and .
Step 5.6.2.1.4
Simplify the expression.
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Step 5.6.2.1.4.1
Multiply by .
Step 5.6.2.1.4.2
Move the negative in front of the fraction.
Step 6
List all of the solutions.
Step 7
The result can be shown in multiple forms.
Exact Form:
Decimal Form: