Solve for x 6|2x+5|=6x+24

$6 | 2 x + 5 | = 6 x + 24$

Divide each term in $6 | 2 x + 5 | = 6 x + 24$ by $6$ and simplify.

Divide each term in $6 | 2 x + 5 | = 6 x + 24$ by $6$ .

$\frac{6 | 2 x + 5 |}{6} = \frac{6 x}{6} + \frac{24}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 | 2 x + 5 |}{6} = \frac{6 x}{6} + \frac{24}{6}$

Divide $| 2 x + 5 |$ by $1$ .

$| 2 x + 5 | = \frac{6 x}{6} + \frac{24}{6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ .

Cancel the common factor.

$| 2 x + 5 | = \frac{6 x}{6} + \frac{24}{6}$

Divide $x$ by $1$ .

$| 2 x + 5 | = x + \frac{24}{6}$

Divide $24$ by $6$ .

$| 2 x + 5 | = x + 4$

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

$2 x + 5 = \pm (x + 4)$

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.

$2 x + 5 = x + 4$

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

Subtract $x$ from both sides of the equation.

$2 x + 5 - x = 4$

Subtract $x$ from $2 x$ .

$x + 5 = 4$

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

Subtract $5$ from both sides of the equation.

$x = 4 - 5$

Subtract $5$ from $4$ .

$x = - 1$

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

$2 x + 5 = - (x + 4)$

Simplify $- (x + 4)$ .

Rewrite.

$2 x + 5 = 0 + 0 - (x + 4)$

Simplify by adding zeros.

$2 x + 5 = - (x + 4)$

Apply the distributive property.

$2 x + 5 = - x - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$2 x + 5 = - x - 4$

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

Add $x$ to both sides of the equation.

$2 x + 5 + x = - 4$

Add $2 x$ and $x$ .

$3 x + 5 = - 4$

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

Subtract $5$ from both sides of the equation.

$3 x = - 4 - 5$

Subtract $5$ from $- 4$ .

$3 x = - 9$

Divide each term in $3 x = - 9$ by $3$ and simplify.

Divide each term in $3 x = - 9$ by $3$ .

$\frac{3 x}{3} = \frac{- 9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 9}{3}$

Divide $x$ by $1$ .

$x = \frac{- 9}{3}$

Simplify the right side.

Divide $- 9$ by $3$ .

$x = - 3$

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

$x = - 1, - 3$

Solve for x 6|2x+5|=6x+24

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