Precalculus Examples

$| 3 - x | = 5$

Step 1

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

$3 - x = \pm 5$

Step 2

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

Tap for more steps...

Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$3 - x = 5$

Step 2.2

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

Tap for more steps...

Step 2.2.1

Subtract $3$ from both sides of the equation.

$- x = 5 - 3$

Step 2.2.2

Subtract $3$ from $5$ .

$- x = 2$

Step 2.3

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

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Dividing two negative values results in a positive value.

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

Step 2.3.2.2

Divide $x$ by $1$ .

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

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Divide $2$ by $- 1$ .

$x = - 2$

Step 2.4

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

$3 - x = - 5$

Step 2.5

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

Tap for more steps...

Step 2.5.1

Subtract $3$ from both sides of the equation.

$- x = - 5 - 3$

Step 2.5.2

Subtract $3$ from $- 5$ .

$- x = - 8$

Step 2.6

Divide each term in $- x = - 8$ by $- 1$ and simplify.

Tap for more steps...

Step 2.6.1

Divide each term in $- x = - 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 8}{- 1}$

Step 2.6.2

Simplify the left side.

Tap for more steps...

Step 2.6.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 8}{- 1}$

Step 2.6.2.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 1}$

Step 2.6.3

Simplify the right side.

Tap for more steps...

Step 2.6.3.1

Divide $- 8$ by $- 1$ .

$x = 8$

Step 2.7

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

$x = - 2, 8$