Solve the Inequality for z -2/3>z/5

$- \frac{2}{3} > \frac{z}{5}$

Multiply both sides by $5$ .

$- \frac{2}{3} \cdot 5 > \frac{z}{5} \cdot 5$

Simplify.

Simplify the left side.

Simplify $- \frac{2}{3} \cdot 5$ .

Multiply $- \frac{2}{3} \cdot 5$ .

Multiply $5$ by $- 1$ .

$- 5 (\frac{2}{3}) > \frac{z}{5} \cdot 5$

Combine $- 5$ and $\frac{2}{3}$ .

$\frac{- 5 \cdot 2}{3} > \frac{z}{5} \cdot 5$

Multiply $- 5$ by $2$ .

$\frac{- 10}{3} > \frac{z}{5} \cdot 5$

$\frac{- 10}{3} > \frac{z}{5} \cdot 5$

Move the negative in front of the fraction.

$- \frac{10}{3} > \frac{z}{5} \cdot 5$

$- \frac{10}{3} > \frac{z}{5} \cdot 5$

$- \frac{10}{3} > \frac{z}{5} \cdot 5$

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

$- \frac{10}{3} > \frac{z}{5} \cdot 5$

Rewrite the expression.

$- \frac{10}{3} > z$

$- \frac{10}{3} > z$

$- \frac{10}{3} > z$

$- \frac{10}{3} > z$

Rewrite so $z$ is on the left side of the inequality.

$z < - \frac{10}{3}$

The result can be shown in multiple forms.

Inequality Form:

$z < - \frac{10}{3}$

Interval Notation:

$(- \infty, - \frac{10}{3})$

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