Solve for x |3x+2|+4x=6

$| 3 x + 2 | + 4 x = 6$

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

$| 3 x + 2 | = 6 - 4 x$

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

$3 x + 2 = \pm (6 - 4 x)$

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.

$3 x + 2 = 6 - 4 x$

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

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

$3 x + 2 + 4 x = 6$

Add $3 x$ and $4 x$ .

$7 x + 2 = 6$

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

Subtract $2$ from both sides of the equation.

$7 x = 6 - 2$

Subtract $2$ from $6$ .

$7 x = 4$

Divide each term in $7 x = 4$ by $7$ and simplify.

Divide each term in $7 x = 4$ by $7$ .

$\frac{7 x}{7} = \frac{4}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{4}{7}$

Divide $x$ by $1$ .

$x = \frac{4}{7}$

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

$3 x + 2 = - (6 - 4 x)$

Simplify $- (6 - 4 x)$ .

Rewrite.

$3 x + 2 = 0 + 0 - (6 - 4 x)$

Simplify by adding zeros.

$3 x + 2 = - (6 - 4 x)$

Apply the distributive property.

$3 x + 2 = - 1 \cdot 6 - (- 4 x)$

Multiply.

Multiply $- 1$ by $6$ .

$3 x + 2 = - 6 - (- 4 x)$

Multiply $- 4$ by $- 1$ .

$3 x + 2 = - 6 + 4 x$

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

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

$3 x + 2 - 4 x = - 6$

Subtract $4 x$ from $3 x$ .

$- x + 2 = - 6$

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

Subtract $2$ from both sides of the equation.

$- x = - 6 - 2$

Subtract $2$ from $- 6$ .

$- x = - 8$

Divide each term in $- x = - 8$ by $- 1$ and simplify.

Divide each term in $- x = - 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 8}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 8}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 8}{- 1}$

Simplify the right side.

Divide $- 8$ by $- 1$ .

$x = 8$

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

$x = \frac{4}{7}, 8$

Exclude the solutions that do not make $| 3 x + 2 | + 4 x = 6$ true.

$x = \frac{4}{7}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4}{7}$

Decimal Form:

$x = 0.\overline{571428}$

Solve for x |3x+2|+4x=6

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