Solve for x 4|3x+4|=4x+8

$4 | 3 x + 4 | = 4 x + 8$

Step 1

Divide each term in $4 | 3 x + 4 | = 4 x + 8$ by $4$ and simplify.

Divide each term in $4 | 3 x + 4 | = 4 x + 8$ by $4$ .

$\frac{4 | 3 x + 4 |}{4} = \frac{4 x}{4} + \frac{8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 | 3 x + 4 |}{4} = \frac{4 x}{4} + \frac{8}{4}$

Divide $| 3 x + 4 |$ by $1$ .

$| 3 x + 4 | = \frac{4 x}{4} + \frac{8}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $4$ .

Cancel the common factor.

$| 3 x + 4 | = \frac{4 x}{4} + \frac{8}{4}$

Divide $x$ by $1$ .

$| 3 x + 4 | = x + \frac{8}{4}$

Divide $8$ by $4$ .

$| 3 x + 4 | = x + 2$

Step 2

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

$3 x + 4 = \pm (x + 2)$

Step 3

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.

$3 x + 4 = x + 2$

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

Subtract $x$ from both sides of the equation.

$3 x + 4 - x = 2$

Subtract $x$ from $3 x$ .

$2 x + 4 = 2$

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

Subtract $4$ from both sides of the equation.

$2 x = 2 - 4$

Subtract $4$ from $2$ .

$2 x = - 2$

Divide each term in $2 x = - 2$ by $2$ and simplify.

Divide each term in $2 x = - 2$ by $2$ .

$\frac{2 x}{2} = \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 2}{2}$

Divide $x$ by $1$ .

$x = \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$x = - 1$

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

$3 x + 4 = - (x + 2)$

Simplify $- (x + 2)$ .

Rewrite.

$3 x + 4 = 0 + 0 - (x + 2)$

Simplify by adding zeros.

$3 x + 4 = - (x + 2)$

Apply the distributive property.

$3 x + 4 = - x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$3 x + 4 = - x - 2$

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

Add $x$ to both sides of the equation.

$3 x + 4 + x = - 2$

Add $3 x$ and $x$ .

$4 x + 4 = - 2$

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

Subtract $4$ from both sides of the equation.

$4 x = - 2 - 4$

Subtract $4$ from $- 2$ .

$4 x = - 6$

Divide each term in $4 x = - 6$ by $4$ and simplify.

Divide each term in $4 x = - 6$ by $4$ .

$\frac{4 x}{4} = \frac{- 6}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 6}{4}$

Divide $x$ by $1$ .

$x = \frac{- 6}{4}$

Simplify the right side.

Cancel the common factor of $- 6$ and $4$ .

Factor $2$ out of $- 6$ .

$x = \frac{2 (- 3)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

$x = - 1, - \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 1, - \frac{3}{2}$

Decimal Form:

$x = - 1, - 1.5$

Mixed Number Form:

$x = - 1, - 1 \frac{1}{2}$

Solve for x 4|3x+4|=4x+8

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