Solve for x |3x+5|=1

$| 3 x + 5 | = 1$

Step 1

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

$3 x + 5 = \pm 1$

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.

$3 x + 5 = 1$

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

Subtract $5$ from both sides of the equation.

$3 x = 1 - 5$

Subtract $5$ from $1$ .

$3 x = - 4$

Divide each term in $3 x = - 4$ by $3$ and simplify.

Divide each term in $3 x = - 4$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

$3 x + 5 = - 1$

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

Subtract $5$ from both sides of the equation.

$3 x = - 1 - 5$

Subtract $5$ from $- 1$ .

$3 x = - 6$

Divide each term in $3 x = - 6$ by $3$ and simplify.

Divide each term in $3 x = - 6$ by $3$ .

$\frac{3 x}{3} = \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 6}{3}$

Divide $x$ by $1$ .

$x = \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$x = - 2$

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 1.\overline{3}, - 2$

Mixed Number Form:

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

Solve for x |3x+5|=1

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