Solve the Inequality for z 5/8z>5/6

$\frac{5}{8} z > \frac{5}{6}$

Step 1

Multiply each term in $\frac{5}{8} z > \frac{5}{6}$ by $\frac{8}{5}$ .

$\frac{5}{8} z \frac{8}{5} > \frac{5}{6} \cdot \frac{8}{5}$

Step 2

Simplify the left side.

Combine $\frac{5}{8}$ and $z$ .

$\frac{5 z}{8} \cdot \frac{8}{5} > \frac{5}{6} \cdot \frac{8}{5}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 z$ .

$\frac{5 (z)}{8} \cdot \frac{8}{5} > \frac{5}{6} \cdot \frac{8}{5}$

Cancel the common factor.

$\frac{5 z}{8} \cdot \frac{8}{5} > \frac{5}{6} \cdot \frac{8}{5}$

Rewrite the expression.

$\frac{z}{8} \cdot 8 > \frac{5}{6} \cdot \frac{8}{5}$

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{z}{8} \cdot 8 > \frac{5}{6} \cdot \frac{8}{5}$

Rewrite the expression.

$z > \frac{5}{6} \cdot \frac{8}{5}$

Step 3

Simplify the right side.

Cancel the common factor of $5$ .

Cancel the common factor.

$z > \frac{5}{6} \cdot \frac{8}{5}$

Rewrite the expression.

$z > \frac{1}{6} \cdot 8$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$z > \frac{1}{2 (3)} \cdot 8$

Factor $2$ out of $8$ .

$z > \frac{1}{2 \cdot 3} \cdot (2 \cdot 4)$

Cancel the common factor.

$z > \frac{1}{2 \cdot 3} \cdot (2 \cdot 4)$

Rewrite the expression.

$z > \frac{1}{3} \cdot 4$

Combine $\frac{1}{3}$ and $4$ .

$z > \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$z > \frac{4}{3}$

Interval Notation:

$(\frac{4}{3}, \infty)$