Solve for x |5x+8|=x

$| 5 x + 8 | = x$

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

$5 x + 8 = \pm x$

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.

$5 x + 8 = x$

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

Subtract $x$ from both sides of the equation.

$5 x + 8 - x = 0$

Subtract $x$ from $5 x$ .

$4 x + 8 = 0$

Subtract $8$ from both sides of the equation.

$4 x = - 8$

Divide each term in $4 x = - 8$ by $4$ and simplify.

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = - 2$

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

$5 x + 8 = - x$

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

Add $x$ to both sides of the equation.

$5 x + 8 + x = 0$

Add $5 x$ and $x$ .

$6 x + 8 = 0$

Subtract $8$ from both sides of the equation.

$6 x = - 8$

Divide each term in $6 x = - 8$ by $6$ and simplify.

Divide each term in $6 x = - 8$ by $6$ .

$\frac{6 x}{6} = \frac{- 8}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 8}{6}$

Divide $x$ by $1$ .

$x = \frac{- 8}{6}$

Simplify the right side.

Cancel the common factor of $- 8$ and $6$ .

Factor $2$ out of $- 8$ .

$x = \frac{2 (- 4)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 \cdot - 4}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 \cdot - 4}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{- 4}{3}$

Move the negative in front of the fraction.

$x = - \frac{4}{3}$

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

$x = - 2, - \frac{4}{3}$

Exclude the solutions that do not make $| 5 x + 8 | = x$ true.

$No solution$

Solve for x |5x+8|=x

Related Questions

Support LCMGCF.com by disabling your adblocker.