Solve the Inequality for z 5z-2-2z<13

$5 z - 2 - 2 z < 13$

Step 1

Subtract $2 z$ from $5 z$ .

$3 z - 2 < 13$

Step 2

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

Add $2$ to both sides of the inequality.

$3 z < 13 + 2$

Add $13$ and $2$ .

$3 z < 15$

Step 3

Divide each term in $3 z < 15$ by $3$ and simplify.

Divide each term in $3 z < 15$ by $3$ .

$\frac{3 z}{3} < \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 z}{3} < \frac{15}{3}$

Divide $z$ by $1$ .

$z < \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

$z < 5$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$z < 5$

Interval Notation:

$(- \infty, 5)$