Pre-Algebra Examples

$x - \frac{1}{3} > \frac{1}{2}$

Step 1

Add $\frac{1}{3}$ to both sides of the inequality.

$x > \frac{1}{2} + \frac{1}{3}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x > \frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3}$

Step 3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x > \frac{1}{2} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$x > \frac{3}{2 \cdot 3} + \frac{1}{3} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $3$ .

$x > \frac{3}{6} + \frac{1}{3} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$x > \frac{3}{6} + \frac{2}{3 \cdot 2}$

Step 4.4

Multiply $3$ by $2$ .

$x > \frac{3}{6} + \frac{2}{6}$

Step 5

Combine the numerators over the common denominator.

$x > \frac{3 + 2}{6}$

Step 6

Add $3$ and $2$ .

$x > \frac{5}{6}$

Step 7