Solve for x |3-2x|=4

$| 3 - 2 x | = 4$

Step 1

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

$3 - 2 x = \pm 4$

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.

$3 - 2 x = 4$

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

Subtract $3$ from both sides of the equation.

$- 2 x = 4 - 3$

Subtract $3$ from $4$ .

$- 2 x = 1$

Divide each term in $- 2 x = 1$ by $- 2$ and simplify.

Divide each term in $- 2 x = 1$ by $- 2$ .

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

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

$3 - 2 x = - 4$

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

Subtract $3$ from both sides of the equation.

$- 2 x = - 4 - 3$

Subtract $3$ from $- 4$ .

$- 2 x = - 7$

Divide each term in $- 2 x = - 7$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 7$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 7}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 7}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 2}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{7}{2}$

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

$x = - \frac{1}{2}, \frac{7}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}, \frac{7}{2}$

Decimal Form:

$x = - 0.5, 3.5$

Mixed Number Form:

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

Solve for x |3-2x|=4

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