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

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

Simplify .

Simplify each term.

Apply the distributive property.

Multiply by .

Add and .

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

Subtract from both sides of the equation.

Combine the opposite terms in .

Subtract from .

Subtract from .

Since , the equation will always be true.

All real numbers

All real numbers

Simplify .

Simplify each term.

Apply the distributive property.

Multiply by .

Add and .

Simplify .

Apply the distributive property.

Multiply.

Multiply by .

Multiply by .

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

Add to both sides of the equation.

Add and .

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

Add to both sides of the equation.

Add and .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

List all of the solutions.

Verify each of the solutions by substituting them into and solving.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Mixed Number Form:

Solve for x |3(x-4)+7|=|3x-5|