Find All Complex Solutions 4|0.5x-2.5|=0

$4 | 0.5 x - 2.5 | = 0$

Step 1

Factor $0.5$ out of $0.5 x - 2.5$ .

Factor $0.5$ out of $0.5 x$ .

$4 | 0.5 (x) - 2.5 | = 0$

Factor $0.5$ out of $- 2.5$ .

$4 | 0.5 x + 0.5 \cdot - 5 | = 0$

Factor $0.5$ out of $0.5 x + 0.5 \cdot - 5$ .

$4 | 0.5 (x - 5) | = 0$

Step 2

Divide each term in $4 | 0.5 (x - 5) | = 0$ by $4$ and simplify.

Divide each term in $4 | 0.5 (x - 5) | = 0$ by $4$ .

$\frac{4 | 0.5 (x - 5) |}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 | 0.5 (x - 5) |}{4} = \frac{0}{4}$

Divide $| 0.5 (x - 5) |$ by $1$ .

$| 0.5 (x - 5) | = \frac{0}{4}$

Apply the distributive property.

$| 0.5 x + 0.5 \cdot - 5 | = \frac{0}{4}$

Multiply $0.5$ by $- 5$ .

$| 0.5 x - 2.5 | = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$| 0.5 x - 2.5 | = 0$

Step 3

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

$0.5 x - 2.5 = \pm 0$

Step 4

Plus or minus $0$ is $0$ .

$0.5 x - 2.5 = 0$

Step 5

Add $2.5$ to both sides of the equation.

$0.5 x = 2.5$

Step 6

Divide each term in $0.5 x = 2.5$ by $0.5$ and simplify.

Divide each term in $0.5 x = 2.5$ by $0.5$ .

$\frac{0.5 x}{0.5} = \frac{2.5}{0.5}$

Simplify the left side.

Cancel the common factor of $0.5$ .

Cancel the common factor.

$\frac{0.5 x}{0.5} = \frac{2.5}{0.5}$

Divide $x$ by $1$ .

$x = \frac{2.5}{0.5}$

Simplify the right side.

Divide $2.5$ by $0.5$ .

$x = 5$

Find All Complex Solutions 4|0.5x-2.5|=0

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