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

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

Step 1

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

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

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.

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

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

Add $3$ to both sides of the equation.

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

Add $1$ and $3$ .

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

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 \cdot 4$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x}{4} = 4 \cdot 4$

Rewrite the expression.

$x = 4 \cdot 4$

Simplify the right side.

Multiply $4$ by $4$ .

$x = 16$

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

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

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

Add $3$ to both sides of the equation.

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

Add $- 1$ and $3$ .

$\frac{x}{4} = 2$

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x}{4} = 4 \cdot 2$

Rewrite the expression.

$x = 4 \cdot 2$

Simplify the right side.

Multiply $4$ by $2$ .

$x = 8$

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

$x = 16, 8$

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

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