Find All Complex Solutions 4|x+1/3|=20

$4 | x + \frac{1}{3} | = 20$

Step 1

Subtract $20$ from both sides of the equation.

$4 | x + \frac{1}{3} | - 20 = 0$

Step 2

Factor $4$ out of $4 | x + \frac{1}{3} | - 20$ .

Factor $4$ out of $4 | x + \frac{1}{3} |$ .

$4 (| x + \frac{1}{3} |) - 20 = 0$

Factor $4$ out of $- 20$ .

$4 | x + \frac{1}{3} | + 4 \cdot - 5 = 0$

Factor $4$ out of $4 | x + \frac{1}{3} | + 4 \cdot - 5$ .

$4 (| x + \frac{1}{3} | - 5) = 0$

Step 3

Divide each term in $4 (| x + \frac{1}{3} | - 5) = 0$ by $4$ and simplify.

Divide each term in $4 (| x + \frac{1}{3} | - 5) = 0$ by $4$ .

$\frac{4 (| x + \frac{1}{3} | - 5)}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 (| x + \frac{1}{3} | - 5)}{4} = \frac{0}{4}$

Divide $| x + \frac{1}{3} | - 5$ by $1$ .

$| x + \frac{1}{3} | - 5 = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$| x + \frac{1}{3} | - 5 = 0$

Step 4

Add $5$ to both sides of the equation.

$| x + \frac{1}{3} | = 5$

Step 5

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

$x + \frac{1}{3} = \pm 5$

Step 6

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.

$x + \frac{1}{3} = 5$

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

Subtract $\frac{1}{3}$ from both sides of the equation.

$x = 5 - \frac{1}{3}$

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = 5 \cdot \frac{3}{3} - \frac{1}{3}$

Combine $5$ and $\frac{3}{3}$ .

$x = \frac{5 \cdot 3}{3} - \frac{1}{3}$

Combine the numerators over the common denominator.

$x = \frac{5 \cdot 3 - 1}{3}$

Simplify the numerator.

Multiply $5$ by $3$ .

$x = \frac{15 - 1}{3}$

Subtract $1$ from $15$ .

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

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

$x + \frac{1}{3} = - 5$

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

Subtract $\frac{1}{3}$ from both sides of the equation.

$x = - 5 - \frac{1}{3}$

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = - 5 \cdot \frac{3}{3} - \frac{1}{3}$

Combine $- 5$ and $\frac{3}{3}$ .

$x = \frac{- 5 \cdot 3}{3} - \frac{1}{3}$

Combine the numerators over the common denominator.

$x = \frac{- 5 \cdot 3 - 1}{3}$

Simplify the numerator.

Multiply $- 5$ by $3$ .

$x = \frac{- 15 - 1}{3}$

Subtract $1$ from $- 15$ .

$x = \frac{- 16}{3}$

Move the negative in front of the fraction.

$x = - \frac{16}{3}$

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

$x = \frac{14}{3}, - \frac{16}{3}$

Find All Complex Solutions 4|x+1/3|=20

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