Algebra Examples

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

Step 1

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

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

Step 2

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

$2 x \cdot \frac{2}{2} - \frac{x}{2}$

Step 3

Simplify terms.

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Step 3.1

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

$\frac{2 x \cdot 2}{2} - \frac{x}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 - x}{2}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $x$ out of $2 x \cdot 2 - x$ .

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Step 4.1.1

Factor $x$ out of $2 x \cdot 2$ .

$\frac{x (2 \cdot 2) - x}{2}$

Step 4.1.2

Factor $x$ out of $- x$ .

$\frac{x (2 \cdot 2) + x \cdot - 1}{2}$

Step 4.1.3

Factor $x$ out of $x (2 \cdot 2) + x \cdot - 1$ .

$\frac{x (2 \cdot 2 - 1)}{2}$

Step 4.2

Multiply $2$ by $2$ .

$\frac{x (4 - 1)}{2}$

Step 4.3

Subtract $1$ from $4$ .

$\frac{x \cdot 3}{2}$

Step 5

Move $3$ to the left of $x$ .

$\frac{3 x}{2}$