Solve for x |3x+5|=7

$| 3 x + 5 | = 7$

Step 1

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

$3 x + 5 = \pm 7$

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.

$3 x + 5 = 7$

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

Subtract $5$ from both sides of the equation.

$3 x = 7 - 5$

Subtract $5$ from $7$ .

$3 x = 2$

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

Divide each term in $3 x = 2$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

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

$3 x + 5 = - 7$

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

Subtract $5$ from both sides of the equation.

$3 x = - 7 - 5$

Subtract $5$ from $- 7$ .

$3 x = - 12$

Divide each term in $3 x = - 12$ by $3$ and simplify.

Divide each term in $3 x = - 12$ by $3$ .

$\frac{3 x}{3} = \frac{- 12}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 12}{3}$

Divide $x$ by $1$ .

$x = \frac{- 12}{3}$

Simplify the right side.

Divide $- 12$ by $3$ .

$x = - 4$

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

$x = \frac{2}{3}, - 4$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}, - 4$

Decimal Form:

$x = 0.\overline{6}, - 4$

Solve for x |3x+5|=7

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