Precalculus Examples

$| x - 1 | + 2 = 5$

Step 1

Move all terms not containing $| x - 1 |$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $2$ from both sides of the equation.

$| x - 1 | = 5 - 2$

Step 1.2

Subtract $2$ from $5$ .

$| x - 1 | = 3$

Step 2

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

$x - 1 = \pm 3$

Step 3

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

Tap for more steps...

Step 3.1

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

$x - 1 = 3$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Add $1$ to both sides of the equation.

$x = 3 + 1$

Step 3.2.2

Add $3$ and $1$ .

$x = 4$

Step 3.3

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

$x - 1 = - 3$

Step 3.4

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

Tap for more steps...

Step 3.4.1

Add $1$ to both sides of the equation.

$x = - 3 + 1$

Step 3.4.2

Add $- 3$ and $1$ .

$x = - 2$

Step 3.5

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

$x = 4, - 2$