Solve for q q-1/2>1/3

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

Step 1

Add $\frac{1}{2}$ to both sides of the inequality.

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

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

Multiply $3$ by $2$ .

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

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

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

Multiply $2$ by $3$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Add $2$ and $3$ .

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

Step 7

The result can be shown in multiple forms.

Inequality Form:

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

Interval Notation:

$(\frac{5}{6}, \infty)$