Pre-Algebra Examples

$x + \frac{1}{2} x = 15$

Step 1

Simplify $x + \frac{1}{2} x$ .

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Step 1.1

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

$x + \frac{x}{2} = 15$

Step 1.2

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

$x \cdot \frac{2}{2} + \frac{x}{2} = 15$

Step 1.3

Simplify terms.

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Step 1.3.1

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

$\frac{x \cdot 2}{2} + \frac{x}{2} = 15$

Step 1.3.2

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x}{2} = 15$

Step 1.4

Simplify the numerator.

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Step 1.4.1

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

$\frac{2 \cdot x + x}{2} = 15$

Step 1.4.2

Add $2 x$ and $x$ .

$\frac{3 x}{2} = 15$

Step 2

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

$x = 10$

Step 3