Solve for x |72+3x|=9x

$| 72 + 3 x | = 9 x$

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

$72 + 3 x = \pm 9 x$

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.

$72 + 3 x = 9 x$

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

Subtract $9 x$ from both sides of the equation.

$72 + 3 x - 9 x = 0$

Subtract $9 x$ from $3 x$ .

$72 - 6 x = 0$

Subtract $72$ from both sides of the equation.

$- 6 x = - 72$

Divide each term in $- 6 x = - 72$ by $- 6$ and simplify.

Divide each term in $- 6 x = - 72$ by $- 6$ .

$\frac{- 6 x}{- 6} = \frac{- 72}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 x}{- 6} = \frac{- 72}{- 6}$

Divide $x$ by $1$ .

$x = \frac{- 72}{- 6}$

Simplify the right side.

Divide $- 72$ by $- 6$ .

$x = 12$

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

$72 + 3 x = - 9 x$

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

Add $9 x$ to both sides of the equation.

$72 + 3 x + 9 x = 0$

Add $3 x$ and $9 x$ .

$72 + 12 x = 0$

Subtract $72$ from both sides of the equation.

$12 x = - 72$

Divide each term in $12 x = - 72$ by $12$ and simplify.

Divide each term in $12 x = - 72$ by $12$ .

$\frac{12 x}{12} = \frac{- 72}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{- 72}{12}$

Divide $x$ by $1$ .

$x = \frac{- 72}{12}$

Simplify the right side.

Divide $- 72$ by $12$ .

$x = - 6$

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

$x = 12, - 6$

Exclude the solutions that do not make $| 72 + 3 x | = 9 x$ true.

$x = 12$

Solve for x |72+3x|=9x

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