Solve for x |3-2x|-5x=3

$| 3 - 2 x | - 5 x = 3$

Add $5 x$ to both sides of the equation.

$| 3 - 2 x | = 3 + 5 x$

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

$3 - 2 x = \pm (3 + 5 x)$

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.

$3 - 2 x = 3 + 5 x$

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

Subtract $5 x$ from both sides of the equation.

$3 - 2 x - 5 x = 3$

Subtract $5 x$ from $- 2 x$ .

$3 - 7 x = 3$

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

Subtract $3$ from both sides of the equation.

$- 7 x = 3 - 3$

Subtract $3$ from $3$ .

$- 7 x = 0$

Divide each term in $- 7 x = 0$ by $- 7$ and simplify.

Divide each term in $- 7 x = 0$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{0}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{0}{- 7}$

Divide $x$ by $1$ .

$x = \frac{0}{- 7}$

Simplify the right side.

Divide $0$ by $- 7$ .

$x = 0$

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

$3 - 2 x = - (3 + 5 x)$

Simplify $- (3 + 5 x)$ .

Rewrite.

$3 - 2 x = 0 + 0 - (3 + 5 x)$

Simplify by adding zeros.

$3 - 2 x = - (3 + 5 x)$

Apply the distributive property.

$3 - 2 x = - 1 \cdot 3 - (5 x)$

Multiply.

Multiply $- 1$ by $3$ .

$3 - 2 x = - 3 - (5 x)$

Multiply $5$ by $- 1$ .

$3 - 2 x = - 3 - 5 x$

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

Add $5 x$ to both sides of the equation.

$3 - 2 x + 5 x = - 3$

Add $- 2 x$ and $5 x$ .

$3 + 3 x = - 3$

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

Subtract $3$ from both sides of the equation.

$3 x = - 3 - 3$

Subtract $3$ from $- 3$ .

$3 x = - 6$

Divide each term in $3 x = - 6$ by $3$ and simplify.

Divide each term in $3 x = - 6$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 6$ by $3$ .

$x = - 2$

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

$x = 0, - 2$

Exclude the solutions that do not make $| 3 - 2 x | - 5 x = 3$ true.

$x = 0$

Solve for x |3-2x|-5x=3

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