Solve the Absolute Value Inequality for x |5x+9|=4x

$| 5 x + 9 | = 4 x$

Step 1

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

$5 x + 9 = \pm 4 x$

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.

$5 x + 9 = 4 x$

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

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

$5 x + 9 - 4 x = 0$

Subtract $4 x$ from $5 x$ .

$x + 9 = 0$

Subtract $9$ from both sides of the equation.

$x = - 9$

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

$5 x + 9 = - 4 x$

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

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

$5 x + 9 + 4 x = 0$

Add $5 x$ and $4 x$ .

$9 x + 9 = 0$

Subtract $9$ from both sides of the equation.

$9 x = - 9$

Divide each term in $9 x = - 9$ by $9$ and simplify.

Divide each term in $9 x = - 9$ by $9$ .

$\frac{9 x}{9} = \frac{- 9}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 9}{9}$

Divide $x$ by $1$ .

$x = \frac{- 9}{9}$

Simplify the right side.

Divide $- 9$ by $9$ .

$x = - 1$

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

$x = - 9, - 1$

Step 3

Exclude the solutions that do not make $| 5 x + 9 | = 4 x$ true.

$No solution$