Trigonometry Examples

$| x - 3 | + 8 = 9$

Step 1

Move all terms not containing $| x - 3 |$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $8$ from both sides of the equation.

$| x - 3 | = 9 - 8$

Step 1.2

Subtract $8$ from $9$ .

$| x - 3 | = 1$

Step 2

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

$x - 3 = \pm 1$

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.

$x - 3 = 1$

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 $3$ to both sides of the equation.

$x = 1 + 3$

Step 3.2.2

Add $1$ and $3$ .

$x = 4$

Step 3.3

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

$x - 3 = - 1$

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 $3$ to both sides of the equation.

$x = - 1 + 3$

Step 3.4.2

Add $- 1$ and $3$ .

$x = 2$

Step 3.5

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

$x = 4, 2$