Solve the Absolute Value Inequality for x |1/3x+4|=3

$| \frac{1}{3} x + 4 | = 3$

Step 1

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

$\frac{1}{3} x + 4 = \pm 3$

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.

$\frac{1}{3} x + 4 = 3$

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

$\frac{x}{3} + 4 = 3$

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

Subtract $4$ from both sides of the equation.

$\frac{x}{3} = 3 - 4$

Subtract $4$ from $3$ .

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

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 \cdot - 1$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot - 1$

Rewrite the expression.

$x = 3 \cdot - 1$

Simplify the right side.

Multiply $3$ by $- 1$ .

$x = - 3$

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

$\frac{1}{3} x + 4 = - 3$

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

$\frac{x}{3} + 4 = - 3$

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

Subtract $4$ from both sides of the equation.

$\frac{x}{3} = - 3 - 4$

Subtract $4$ from $- 3$ .

$\frac{x}{3} = - 7$

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 \cdot - 7$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{x}{3} = 3 \cdot - 7$

Rewrite the expression.

$x = 3 \cdot - 7$

Simplify the right side.

Multiply $3$ by $- 7$ .

$x = - 21$

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

$x = - 3, - 21$

Solve the Absolute Value Inequality for x |1/3x+4|=3

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