Solve the Inequality for z 3/5z>3/4

$\frac{3}{5} z > \frac{3}{4}$

Step 1

Multiply each term in $\frac{3}{5} z > \frac{3}{4}$ by $\frac{5}{3}$ .

$\frac{3}{5} z \frac{5}{3} > \frac{3}{4} \cdot \frac{5}{3}$

Step 2

Simplify the left side.

Combine $\frac{3}{5}$ and $z$ .

$\frac{3 z}{5} \cdot \frac{5}{3} > \frac{3}{4} \cdot \frac{5}{3}$

Cancel the common factor of $3$ .

Factor $3$ out of $3 z$ .

$\frac{3 (z)}{5} \cdot \frac{5}{3} > \frac{3}{4} \cdot \frac{5}{3}$

Cancel the common factor.

$\frac{3 z}{5} \cdot \frac{5}{3} > \frac{3}{4} \cdot \frac{5}{3}$

Rewrite the expression.

$\frac{z}{5} \cdot 5 > \frac{3}{4} \cdot \frac{5}{3}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{z}{5} \cdot 5 > \frac{3}{4} \cdot \frac{5}{3}$

Rewrite the expression.

$z > \frac{3}{4} \cdot \frac{5}{3}$

Step 3

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$z > \frac{3}{4} \cdot \frac{5}{3}$

Rewrite the expression.

$z > \frac{1}{4} \cdot 5$

Combine $\frac{1}{4}$ and $5$ .

$z > \frac{5}{4}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$z > \frac{5}{4}$

Interval Notation:

$(\frac{5}{4}, \infty)$