Find All Complex Solutions |2x-8|+3=5

$| 2 x - 8 | + 3 = 5$

Step 1

Move all terms not containing $| 2 x - 8 |$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$| 2 x - 8 | = 5 - 3$

Subtract $3$ from $5$ .

$| 2 x - 8 | = 2$

Step 2

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

$2 x - 8 = \pm 2$

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.

$2 x - 8 = 2$

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

Add $8$ to both sides of the equation.

$2 x = 2 + 8$

Add $2$ and $8$ .

$2 x = 10$

Divide each term in $2 x = 10$ by $2$ and simplify.

Divide each term in $2 x = 10$ by $2$ .

$\frac{2 x}{2} = \frac{10}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{10}{2}$

Divide $x$ by $1$ .

$x = \frac{10}{2}$

Simplify the right side.

Divide $10$ by $2$ .

$x = 5$

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

$2 x - 8 = - 2$

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

Add $8$ to both sides of the equation.

$2 x = - 2 + 8$

Add $- 2$ and $8$ .

$2 x = 6$

Divide each term in $2 x = 6$ by $2$ and simplify.

Divide each term in $2 x = 6$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2}$

Simplify the right side.

Divide $6$ by $2$ .

$x = 3$

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

$x = 5, 3$

Find All Complex Solutions |2x-8|+3=5

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