Algebra Examples

$2 x - \frac{2}{3} \geq x - 22$

Step 1

Move all terms containing $x$ to the left side of the inequality.

Tap for more steps...

Step 1.1

Subtract $x$ from both sides of the inequality.

$2 x - \frac{2}{3} - x \geq - 22$

Step 1.2

Subtract $x$ from $2 x$ .

$x - \frac{2}{3} \geq - 22$

Step 2

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

Tap for more steps...

Step 2.1

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

$x \geq - 22 + \frac{2}{3}$

Step 2.2

To write $- 22$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x \geq - 22 \cdot \frac{3}{3} + \frac{2}{3}$

Step 2.3

Combine $- 22$ and $\frac{3}{3}$ .

$x \geq \frac{- 22 \cdot 3}{3} + \frac{2}{3}$

Step 2.4

Combine the numerators over the common denominator.

$x \geq \frac{- 22 \cdot 3 + 2}{3}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $- 22$ by $3$ .

$x \geq \frac{- 66 + 2}{3}$

Step 2.5.2

Add $- 66$ and $2$ .

$x \geq \frac{- 64}{3}$

Step 2.6

Move the negative in front of the fraction.

$x \geq - \frac{64}{3}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \geq - \frac{64}{3}$

Interval Notation:

$[- \frac{64}{3}, \infty)$