Solve for x |2x-12|=-4x

$| 2 x - 12 | = - 4 x$

Step 1

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

$2 x - 12 = \pm (- 4 x)$

Step 2

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.

$2 x - 12 = - 4 x$

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

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

$2 x - 12 + 4 x = 0$

Add $2 x$ and $4 x$ .

$6 x - 12 = 0$

Add $12$ to both sides of the equation.

$6 x = 12$

Divide each term in $6 x = 12$ by $6$ and simplify.

Divide each term in $6 x = 12$ by $6$ .

$\frac{6 x}{6} = \frac{12}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{12}{6}$

Divide $x$ by $1$ .

$x = \frac{12}{6}$

Simplify the right side.

Divide $12$ by $6$ .

$x = 2$

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

$2 x - 12 = 4 x$

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

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

$2 x - 12 - 4 x = 0$

Subtract $4 x$ from $2 x$ .

$- 2 x - 12 = 0$

Add $12$ to both sides of the equation.

$- 2 x = 12$

Divide each term in $- 2 x = 12$ by $- 2$ and simplify.

Divide each term in $- 2 x = 12$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{12}{- 2}$

Divide $x$ by $1$ .

$x = \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$x = - 6$

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

$x = 2, - 6$

Step 3

Exclude the solutions that do not make $| 2 x - 12 | = - 4 x$ true.

$x = - 6$

Solve for x |2x-12|=-4x

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