Solve the Absolute Value Inequality for x |3x-5|=2x

$| 3 x - 5 | = 2 x$

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

$3 x - 5 = \pm 2 x$

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.

$3 x - 5 = 2 x$

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

Subtract $2 x$ from both sides of the equation.

$3 x - 5 - 2 x = 0$

Subtract $2 x$ from $3 x$ .

$x - 5 = 0$

Add $5$ to both sides of the equation.

$x = 5$

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

$3 x - 5 = - 2 x$

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

Add $2 x$ to both sides of the equation.

$3 x - 5 + 2 x = 0$

Add $3 x$ and $2 x$ .

$5 x - 5 = 0$

Add $5$ to both sides of the equation.

$5 x = 5$

Divide each term in $5 x = 5$ by $5$ and simplify.

Divide each term in $5 x = 5$ by $5$ .

$\frac{5 x}{5} = \frac{5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{5}{5}$

Divide $x$ by $1$ .

$x = \frac{5}{5}$

Simplify the right side.

Divide $5$ by $5$ .

$x = 1$

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

$x = 5, 1$