Graph 1/2x-2/3>2

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

Step 1

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

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

Step 2

Move all terms not containing $x$ to the right side of the inequality.

Add $\frac{2}{3}$ to both sides of the inequality.

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

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

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

Combine $2$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $3$ .

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

Add $6$ and $2$ .

$\frac{x}{2} > \frac{8}{3}$

Step 3

Multiply both sides by $2$ .

$\frac{x}{2} \cdot 2 > \frac{8}{3} \cdot 2$

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 > \frac{8}{3} \cdot 2$

Rewrite the expression.

$x > \frac{8}{3} \cdot 2$

Simplify the right side.

Multiply $\frac{8}{3} \cdot 2$ .

Combine $\frac{8}{3}$ and $2$ .

$x > \frac{8 \cdot 2}{3}$

Multiply $8$ by $2$ .

$x > \frac{16}{3}$

Step 5