Algebra Examples

$\frac{1}{9} z \geq - \frac{2}{3}$

Step 1

Multiply each term in $\frac{1}{9} z \geq - \frac{2}{3}$ by $9$ .

$\frac{1}{9} z \cdot 9 \geq - \frac{2}{3} \cdot 9$

Step 2

Simplify the left side.

Tap for more steps...

Step 2.1

Combine $\frac{1}{9}$ and $z$ .

$\frac{z}{9} \cdot 9 \geq - \frac{2}{3} \cdot 9$

Step 2.2

Cancel the common factor of $9$ .

Tap for more steps...

Step 2.2.1

Cancel the common factor.

$\frac{z}{9} \cdot 9 \geq - \frac{2}{3} \cdot 9$

Step 2.2.2

Rewrite the expression.

$z \geq - \frac{2}{3} \cdot 9$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$z \geq \frac{- 2}{3} \cdot 9$

Step 3.1.2

Factor $3$ out of $9$ .

$z \geq \frac{- 2}{3} \cdot (3 (3))$

Step 3.1.3

Cancel the common factor.

$z \geq \frac{- 2}{3} \cdot (3 \cdot 3)$

Step 3.1.4

Rewrite the expression.

$z \geq - 2 \cdot 3$

Step 3.2

Multiply $- 2$ by $3$ .

$z \geq - 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$z \geq - 6$

Interval Notation:

$[- 6, \infty)$