Solve the Absolute Value Inequality for x |2x-6|=4x

$| 2 x - 6 | = 4 x$

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

$2 x - 6 = \pm 4 x$

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.

$2 x - 6 = 4 x$

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

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

$2 x - 6 - 4 x = 0$

Subtract $4 x$ from $2 x$ .

$- 2 x - 6 = 0$

Add $6$ to both sides of the equation.

$- 2 x = 6$

Divide each term in $- 2 x = 6$ by $- 2$ and simplify.

Divide each term in $- 2 x = 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{6}{- 2}$

Divide $x$ by $1$ .

$x = \frac{6}{- 2}$

Simplify the right side.

Divide $6$ by $- 2$ .

$x = - 3$

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

$2 x - 6 = - 4 x$

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

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

$2 x - 6 + 4 x = 0$

Add $2 x$ and $4 x$ .

$6 x - 6 = 0$

Add $6$ to both sides of the equation.

$6 x = 6$

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

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

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $6$ by $6$ .

$x = 1$

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

$x = - 3, 1$

Exclude the solutions that do not make $| 2 x - 6 | = 4 x$ true.

$x = 1$

Solve the Absolute Value Inequality for x |2x-6|=4x

Related Questions

Support LCMGCF.com by disabling your adblocker.