Solve for x |5x+6|-6=x

$| 5 x + 6 | - 6 = x$

Add $6$ to both sides of the equation.

$| 5 x + 6 | = x + 6$

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

$5 x + 6 = \pm (x + 6)$

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.

$5 x + 6 = x + 6$

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

Subtract $x$ from both sides of the equation.

$5 x + 6 - x = 6$

Subtract $x$ from $5 x$ .

$4 x + 6 = 6$

Move all terms not containing $x$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$4 x = 6 - 6$

Subtract $6$ from $6$ .

$4 x = 0$

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$

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

$5 x + 6 = - (x + 6)$

Simplify $- (x + 6)$ .

Rewrite.

$5 x + 6 = 0 + 0 - (x + 6)$

Simplify by adding zeros.

$5 x + 6 = - (x + 6)$

Apply the distributive property.

$5 x + 6 = - x - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$5 x + 6 = - x - 6$

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

Add $x$ to both sides of the equation.

$5 x + 6 + x = - 6$

Add $5 x$ and $x$ .

$6 x + 6 = - 6$

Move all terms not containing $x$ to the right side of the equation.

Subtract $6$ from both sides of the equation.

$6 x = - 6 - 6$

Subtract $6$ from $- 6$ .

$6 x = - 12$

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 $6$ .

$x = - 2$

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

$x = 0, - 2$

Solve for x |5x+6|-6=x

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