Solve for x 4+|2-3x|=7

$4 + | 2 - 3 x | = 7$

Step 1

Move all terms not containing $| 2 - 3 x |$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$| 2 - 3 x | = 7 - 4$

Subtract $4$ from $7$ .

$| 2 - 3 x | = 3$

Step 2

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

$2 - 3 x = \pm 3$

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.

$2 - 3 x = 3$

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

Subtract $2$ from both sides of the equation.

$- 3 x = 3 - 2$

Subtract $2$ from $3$ .

$- 3 x = 1$

Divide each term in $- 3 x = 1$ by $- 3$ and simplify.

Divide each term in $- 3 x = 1$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

$2 - 3 x = - 3$

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

Subtract $2$ from both sides of the equation.

$- 3 x = - 3 - 2$

Subtract $2$ from $- 3$ .

$- 3 x = - 5$

Divide each term in $- 3 x = - 5$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 5$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 5}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 5}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 5}{- 3}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{5}{3}$

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

$x = - \frac{1}{3}, \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{3}, \frac{5}{3}$

Decimal Form:

$x = - 0.\overline{3}, 1.\overline{6}$

Mixed Number Form:

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

Solve for x 4+|2-3x|=7

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