Solve the Absolute Value Inequality for x (2|x-3|)/5=6

$\frac{2 | x - 3 |}{5} = 6$

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} \cdot \frac{2 | x - 3 |}{5} = \frac{5}{2} \cdot 6$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{2} \cdot \frac{2 | x - 3 |}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{2} \cdot \frac{2 | x - 3 |}{5} = \frac{5}{2} \cdot 6$

Rewrite the expression.

$\frac{1}{2} (2 | x - 3 |) = \frac{5}{2} \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $2 | x - 3 |$ .

$\frac{1}{2} (2 (| x - 3 |)) = \frac{5}{2} \cdot 6$

Cancel the common factor.

$\frac{1}{2} (2 | x - 3 |) = \frac{5}{2} \cdot 6$

Rewrite the expression.

$| x - 3 | = \frac{5}{2} \cdot 6$

Simplify the right side.

Simplify $\frac{5}{2} \cdot 6$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$| x - 3 | = \frac{5}{2} \cdot (2 (3))$

Cancel the common factor.

$| x - 3 | = \frac{5}{2} \cdot (2 \cdot 3)$

Rewrite the expression.

$| x - 3 | = 5 \cdot 3$

Multiply $5$ by $3$ .

$| x - 3 | = 15$

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

$x - 3 = \pm 15$

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.

$x - 3 = 15$

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

Add $3$ to both sides of the equation.

$x = 15 + 3$

Add $15$ and $3$ .

$x = 18$

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

$x - 3 = - 15$

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

Add $3$ to both sides of the equation.

$x = - 15 + 3$

Add $- 15$ and $3$ .

$x = - 12$

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

$x = 18, - 12$

Solve the Absolute Value Inequality for x (2|x-3|)/5=6

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