Solve for x |x-4|=|3x|

$| x - 4 | = | 3 x |$

Step 1

Rewrite the equation as $| 3 x | = | x - 4 |$ .

$| 3 x | = | x - 4 |$

Step 2

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

$3 x = x - 4$

$3 x = - (x - 4)$

$- 1 \cdot (3 x) = x - 4$

$- 1 \cdot (3 x) = - (x - 4)$

Step 3

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

$3 x = x - 4$

$3 x = - (x - 4)$

Step 4

Solve $3 x = x - 4$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$3 x - x = - 4$

Subtract $x$ from $3 x$ .

$2 x = - 4$

Divide each term in $2 x = - 4$ by $2$ and simplify.

Divide each term in $2 x = - 4$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 4$ by $2$ .

$x = - 2$

Step 5

Solve $3 x = - (x - 4)$ for $x$ .

Simplify $- (x - 4)$ .

Apply the distributive property.

$3 x = - x - - 4$

Multiply $- 1$ by $- 4$ .

$3 x = - x + 4$

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

Add $x$ to both sides of the equation.

$3 x + x = 4$

Add $3 x$ and $x$ .

$4 x = 4$

Divide each term in $4 x = 4$ by $4$ and simplify.

Divide each term in $4 x = 4$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $4$ by $4$ .

$x = 1$

Step 6

List all of the solutions.

$x = - 2, 1$

Solve for x |x-4|=|3x|

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