Finite Math Examples

$| x - \frac{1}{2} x | = | \frac{1}{2} x - 2 |$

Step 1

Simplify $| x - \frac{1}{2} x |$ .

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Step 1.1

Combine $x$ and $\frac{1}{2}$ .

$| x - \frac{x}{2} | = | \frac{1}{2} x - 2 |$

Step 1.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.3

Simplify terms.

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Step 1.3.1

Combine $x$ and $\frac{2}{2}$ .

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

Step 1.3.2

Combine the numerators over the common denominator.

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

Step 1.4

Simplify the numerator.

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Step 1.4.1

Move $2$ to the left of $x$ .

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

Step 1.4.2

Subtract $x$ from $2 x$ .

$| \frac{x}{2} | = | \frac{1}{2} x - 2 |$

Step 1.5

Remove non-negative terms from the absolute value.

$\frac{| x |}{2} = | \frac{1}{2} x - 2 |$

Step 2

Combine $\frac{1}{2}$ and $x$ .

$\frac{| x |}{2} = | \frac{x}{2} - 2 |$

Step 3

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 2$

Step 4