Rewrite the absolute value equation as four equations without absolute value bars.

After simplifying, there are only two unique equations to be solved.

Combine and .

Combine and .

Move all terms containing to the left side of the equation.

Subtract from both sides of the equation.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Subtract from .

Reorder and .

Subtract from .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Subtract from .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply both sides of the equation by .

Simplify both sides of the equation.

Simplify .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Simplify .

Combine and .

Apply the distributive property.

Move all terms containing to the left side of the equation.

Add to both sides of the equation.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Add and .

Reorder and .

Add and .

Move all terms not containing to the right side of the equation.

Subtract from both sides of the equation.

To write as a fraction with a common denominator, multiply by .

Multiply and .

Multiply by .

Combine the numerators over the common denominator.

Subtract from .

Move the negative in front of the fraction.

Multiply both sides of the equation by .

Simplify both sides of the equation.

Simplify .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Simplify .

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine and .

Simplify the expression.

Multiply by .

Move the negative in front of the fraction.

List all of the solutions.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for a |1/2a+1/12|=|1/8a+1/3|