Solve for x |4x-15|=|x|

$| 4 x - 15 | = | x |$

Rewrite the equation as $| x | = | 4 x - 15 |$ .

$| x | = | 4 x - 15 |$

Rewrite the absolute value equation as four equations without absolute value bars.

$x = 4 x - 15$

$x = - (4 x - 15)$

$- x = 4 x - 15$

$- x = - (4 x - 15)$

After simplifying, there are only two unique equations to be solved.

$x = 4 x - 15$

$x = - (4 x - 15)$

Solve $x = 4 x - 15$ for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$x - 4 x = - 15$

Subtract $4 x$ from $x$ .

$- 3 x = - 15$

Divide each term in $- 3 x = - 15$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 15$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 15}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 15}{- 3}$

Simplify the right side.

Divide $- 15$ by $- 3$ .

$x = 5$

Solve $x = - (4 x - 15)$ for $x$ .

Simplify $- (4 x - 15)$ .

Apply the distributive property.

$x = - (4 x) - - 15$

Multiply.

Multiply $4$ by $- 1$ .

$x = - 4 x - - 15$

Multiply $- 1$ by $- 15$ .

$x = - 4 x + 15$

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

Add $4 x$ to both sides of the equation.

$x + 4 x = 15$

Add $x$ and $4 x$ .

$5 x = 15$

Divide each term in $5 x = 15$ by $5$ and simplify.

Divide each term in $5 x = 15$ by $5$ .

$\frac{5 x}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{15}{5}$

Divide $x$ by $1$ .

$x = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$x = 3$

List all of the solutions.

$x = 5, 3$

Solve for x |4x-15|=|x|

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