Precalculus Examples

$| 1 - x | = 2$

Step 1

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

$1 - x = \pm 2$

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.

$1 - x = 2$

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 $1$ from both sides of the equation.

$- x = 2 - 1$

Step 2.2.2

Subtract $1$ from $2$ .

$- x = 1$

Step 2.3

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

Tap for more steps...

Step 2.3.1

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

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

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.

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

Step 2.3.2.2

Divide $x$ by $1$ .

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

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Divide $1$ by $- 1$ .

$x = - 1$

Step 2.4

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

$1 - x = - 2$

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 $1$ from both sides of the equation.

$- x = - 2 - 1$

Step 2.5.2

Subtract $1$ from $- 2$ .

$- x = - 3$

Step 2.6

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

Tap for more steps...

Step 2.6.1

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

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

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.

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

Step 2.6.2.2

Divide $x$ by $1$ .

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

Step 2.6.3

Simplify the right side.

Tap for more steps...

Step 2.6.3.1

Divide $- 3$ by $- 1$ .

$x = 3$

Step 2.7

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

$x = - 1, 3$