Basic Math Examples

$| 5 - j | - 3 = 8$

Step 1

Move all terms not containing $| 5 - j |$ to the right side of the equation.

Tap for more steps...

Step 1.1

Add $3$ to both sides of the equation.

$| 5 - j | = 8 + 3$

Step 1.2

Add $8$ and $3$ .

$| 5 - j | = 11$

Step 2

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

$5 - j = \pm 11$

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.

$5 - j = 11$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Subtract $5$ from both sides of the equation.

$- j = 11 - 5$

Step 3.2.2

Subtract $5$ from $11$ .

$- j = 6$

Step 3.3

Divide each term in $- j = 6$ by $- 1$ and simplify.

Tap for more steps...

Step 3.3.1

Divide each term in $- j = 6$ by $- 1$ .

$\frac{- j}{- 1} = \frac{6}{- 1}$

Step 3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.2.1

Dividing two negative values results in a positive value.

$\frac{j}{1} = \frac{6}{- 1}$

Step 3.3.2.2

Divide $j$ by $1$ .

$j = \frac{6}{- 1}$

Step 3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.1

Divide $6$ by $- 1$ .

$j = - 6$

Step 3.4

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

$5 - j = - 11$

Step 3.5

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

Tap for more steps...

Step 3.5.1

Subtract $5$ from both sides of the equation.

$- j = - 11 - 5$

Step 3.5.2

Subtract $5$ from $- 11$ .

$- j = - 16$

Step 3.6

Divide each term in $- j = - 16$ by $- 1$ and simplify.

Tap for more steps...

Step 3.6.1

Divide each term in $- j = - 16$ by $- 1$ .

$\frac{- j}{- 1} = \frac{- 16}{- 1}$

Step 3.6.2

Simplify the left side.

Tap for more steps...

Step 3.6.2.1

Dividing two negative values results in a positive value.

$\frac{j}{1} = \frac{- 16}{- 1}$

Step 3.6.2.2

Divide $j$ by $1$ .

$j = \frac{- 16}{- 1}$

Step 3.6.3

Simplify the right side.

Tap for more steps...

Step 3.6.3.1

Divide $- 16$ by $- 1$ .

$j = 16$

Step 3.7

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

$j = - 6, 16$