Solve for x |3x-2|=2|x+2|

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

Rewrite the equation as $2 | x + 2 | = | 3 x - 2 |$ .

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

Divide each term in $2 | x + 2 | = | 3 x - 2 |$ by $2$ and simplify.

Divide each term in $2 | x + 2 | = | 3 x - 2 |$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

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

Rewrite the absolute value equation as four equations without absolute value bars.

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

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

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

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

After simplifying, there are only two unique equations to be solved.

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

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

Solve $x + 2 = \frac{3 x - 2}{2}$ for $x$ .

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

Simplify $(x + 2) \cdot 2$ .

Apply the distributive property.

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

Simplify the expression.

Move $2$ to the left of $x$ .

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

Multiply $2$ by $2$ .

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

Simplify the right side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2 x + 4 = 3 x - 2$

Solve for $x$ .

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

Subtract $3 x$ from both sides of the equation.

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

Subtract $3 x$ from $2 x$ .

$- x + 4 = - 2$

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

Subtract $4$ from both sides of the equation.

$- x = - 2 - 4$

Subtract $4$ from $- 2$ .

$- x = - 6$

Divide each term in $- x = - 6$ by $- 1$ and simplify.

Divide each term in $- x = - 6$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 6}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 6}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 1}$

Simplify the right side.

Divide $- 6$ by $- 1$ .

$x = 6$

Solve $x + 2 = - \frac{3 x - 2}{2}$ for $x$ .

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

Simplify $(x + 2) \cdot 2$ .

Apply the distributive property.

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

Simplify the expression.

Move $2$ to the left of $x$ .

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

Multiply $2$ by $2$ .

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

Simplify the right side.

Simplify $- \frac{3 x - 2}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3 x - 2}{2}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Apply the distributive property.

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

Multiply.

Multiply $3$ by $- 1$ .

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

Multiply $- 1$ by $- 2$ .

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

Solve for $x$ .

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

Add $3 x$ to both sides of the equation.

$2 x + 4 + 3 x = 2$

Add $2 x$ and $3 x$ .

$5 x + 4 = 2$

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

Subtract $4$ from both sides of the equation.

$5 x = 2 - 4$

Subtract $4$ from $2$ .

$5 x = - 2$

Divide each term in $5 x = - 2$ by $5$ and simplify.

Divide each term in $5 x = - 2$ by $5$ .

$\frac{5 x}{5} = \frac{- 2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 2}{5}$

Divide $x$ by $1$ .

$x = \frac{- 2}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{2}{5}$

List all of the solutions.

$x = 6, - \frac{2}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = 6, - \frac{2}{5}$

Decimal Form:

$x = 6, - 0.4$

Solve for x |3x-2|=2|x+2|

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