Find All Complex Solutions 3|x-9|=13

$3 | x - 9 | = 13$

Step 1

Divide each term in $3 | x - 9 | = 13$ by $3$ and simplify.

Divide each term in $3 | x - 9 | = 13$ by $3$ .

$\frac{3 | x - 9 |}{3} = \frac{13}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 | x - 9 |}{3} = \frac{13}{3}$

Divide $| x - 9 |$ by $1$ .

$| x - 9 | = \frac{13}{3}$

Step 2

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

$x - 9 = \pm \frac{13}{3}$

Step 3

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

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

$x - 9 = \frac{13}{3}$

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

Add $9$ to both sides of the equation.

$x = \frac{13}{3} + 9$

To write $9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{13}{3} + 9 \cdot \frac{3}{3}$

Combine $9$ and $\frac{3}{3}$ .

$x = \frac{13}{3} + \frac{9 \cdot 3}{3}$

Combine the numerators over the common denominator.

$x = \frac{13 + 9 \cdot 3}{3}$

Simplify the numerator.

Multiply $9$ by $3$ .

$x = \frac{13 + 27}{3}$

Add $13$ and $27$ .

$x = \frac{40}{3}$

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

$x - 9 = - \frac{13}{3}$

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

Add $9$ to both sides of the equation.

$x = - \frac{13}{3} + 9$

To write $9$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = - \frac{13}{3} + 9 \cdot \frac{3}{3}$

Combine $9$ and $\frac{3}{3}$ .

$x = - \frac{13}{3} + \frac{9 \cdot 3}{3}$

Combine the numerators over the common denominator.

$x = \frac{- 13 + 9 \cdot 3}{3}$

Simplify the numerator.

Multiply $9$ by $3$ .

$x = \frac{- 13 + 27}{3}$

Add $- 13$ and $27$ .

$x = \frac{14}{3}$

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

$x = \frac{40}{3}, \frac{14}{3}$

Find All Complex Solutions 3|x-9|=13

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