Find All Complex Solutions 1/2|5x-15|=10

$\frac{1}{2} | 5 x - 15 | = 10$

Multiply each term in $\frac{1}{2} | 5 x - 15 | = 10$ by $2$ to eliminate the fractions.

Multiply each term in $\frac{1}{2} | 5 x - 15 | = 10$ by $2$ .

$\frac{1}{2} | 5 x - 15 | \cdot 2 = 10 \cdot 2$

Simplify the left side.

Combine $\frac{1}{2}$ and $| 5 x - 15 |$ .

$\frac{| 5 x - 15 |}{2} \cdot 2 = 10 \cdot 2$

Simplify the numerator.

Factor $5$ out of $5 x - 15$ .

Factor $5$ out of $5 x$ .

$\frac{| 5 (x) - 15 |}{2} \cdot 2 = 10 \cdot 2$

Factor $5$ out of $- 15$ .

$\frac{| 5 x + 5 \cdot - 3 |}{2} \cdot 2 = 10 \cdot 2$

Factor $5$ out of $5 x + 5 \cdot - 3$ .

$\frac{| 5 (x - 3) |}{2} \cdot 2 = 10 \cdot 2$

Apply the distributive property.

$\frac{| 5 x + 5 \cdot - 3 |}{2} \cdot 2 = 10 \cdot 2$

Multiply $5$ by $- 3$ .

$\frac{| 5 x - 15 |}{2} \cdot 2 = 10 \cdot 2$

Factor $5$ out of $5 x - 15$ .

Factor $5$ out of $5 x$ .

$\frac{| 5 (x) - 15 |}{2} \cdot 2 = 10 \cdot 2$

Factor $5$ out of $- 15$ .

$\frac{| 5 x + 5 \cdot - 3 |}{2} \cdot 2 = 10 \cdot 2$

Factor $5$ out of $5 x + 5 \cdot - 3$ .

$\frac{| 5 (x - 3) |}{2} \cdot 2 = 10 \cdot 2$

Remove non-negative terms from the absolute value.

$\frac{5 | x - 3 |}{2} \cdot 2 = 10 \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{5 | x - 3 |}{2} \cdot 2 = 10 \cdot 2$

Rewrite the expression.

$5 | x - 3 | = 10 \cdot 2$

Simplify the right side.

Multiply $10$ by $2$ .

$5 | x - 3 | = 20$

Subtract $20$ from both sides of the equation.

$5 | x - 3 | - 20 = 0$

Factor $5$ out of $5 | x - 3 | - 20$ .

Factor $5$ out of $5 | x - 3 |$ .

$5 (| x - 3 |) - 20 = 0$

Factor $5$ out of $- 20$ .

$5 | x - 3 | + 5 \cdot - 4 = 0$

Factor $5$ out of $5 | x - 3 | + 5 \cdot - 4$ .

$5 (| x - 3 | - 4) = 0$

Divide each term in $5 (| x - 3 | - 4) = 0$ by $5$ and simplify.

Divide each term in $5 (| x - 3 | - 4) = 0$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $| x - 3 | - 4$ by $1$ .

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

Simplify the right side.

Divide $0$ by $5$ .

$| x - 3 | - 4 = 0$

Add $4$ to both sides of the equation.

$| x - 3 | = 4$

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

$x - 3 = \pm 4$

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.

$x - 3 = 4$

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

Add $3$ to both sides of the equation.

$x = 4 + 3$

Add $4$ and $3$ .

$x = 7$

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

$x - 3 = - 4$

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

Add $3$ to both sides of the equation.

$x = - 4 + 3$

Add $- 4$ and $3$ .

$x = - 1$

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

$x = 7, - 1$

Find All Complex Solutions 1/2|5x-15|=10

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