Solve for x |1/3x+3|=6

$| \frac{1}{3} x + 3 | = 6$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$\frac{1}{3} x + 3 = \pm 6$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$\frac{1}{3} x + 3 = 6$

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} + 3 = 6$

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

Subtract $3$ from both sides of the equation.

$\frac{x}{3} = 6 - 3$

Subtract $3$ from $6$ .

$\frac{x}{3} = 3$

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 \cdot 3$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot 3$

Rewrite the expression.

$x = 3 \cdot 3$

Simplify the right side.

Multiply $3$ by $3$ .

$x = 9$

Next, use the negative value of the $\pm$ to find the second solution.

$\frac{1}{3} x + 3 = - 6$

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} + 3 = - 6$

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

Subtract $3$ from both sides of the equation.

$\frac{x}{3} = - 6 - 3$

Subtract $3$ from $- 6$ .

$\frac{x}{3} = - 9$

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 \cdot - 9$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot - 9$

Rewrite the expression.

$x = 3 \cdot - 9$

Simplify the right side.

Multiply $3$ by $- 9$ .

$x = - 27$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 9, - 27$

Solve for x |1/3x+3|=6

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