Algebra Examples

$z - 18 \geq - \frac{2}{3}$

Step 1

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

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Step 1.1

Add $18$ to both sides of the inequality.

$z \geq - \frac{2}{3} + 18$

Step 1.2

To write $18$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$z \geq - \frac{2}{3} + 18 \cdot \frac{3}{3}$

Step 1.3

Combine $18$ and $\frac{3}{3}$ .

$z \geq - \frac{2}{3} + \frac{18 \cdot 3}{3}$

Step 1.4

Combine the numerators over the common denominator.

$z \geq \frac{- 2 + 18 \cdot 3}{3}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $18$ by $3$ .

$z \geq \frac{- 2 + 54}{3}$

Step 1.5.2

Add $- 2$ and $54$ .

$z \geq \frac{52}{3}$

Step 2

Convert the inequality to interval notation.

$[\frac{52}{3}, \infty)$

Step 3