Solve the Inequality for y 3(2y-22)<-5y-33

$3 (2 y - 22) < - 5 y - 33$

Step 1

Simplify $3 (2 y - 22)$ .

Rewrite.

$0 + 0 + 3 (2 y - 22) < - 5 y - 33$

Simplify by adding zeros.

$3 (2 y - 22) < - 5 y - 33$

Apply the distributive property.

$3 (2 y) + 3 \cdot - 22 < - 5 y - 33$

Multiply.

Multiply $2$ by $3$ .

$6 y + 3 \cdot - 22 < - 5 y - 33$

Multiply $3$ by $- 22$ .

$6 y - 66 < - 5 y - 33$

Step 2

Move all terms containing $y$ to the left side of the inequality.

Add $5 y$ to both sides of the inequality.

$6 y - 66 + 5 y < - 33$

Add $6 y$ and $5 y$ .

$11 y - 66 < - 33$

Step 3

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

Add $66$ to both sides of the inequality.

$11 y < - 33 + 66$

Add $- 33$ and $66$ .

$11 y < 33$

Step 4

Divide each term in $11 y < 33$ by $11$ and simplify.

Divide each term in $11 y < 33$ by $11$ .

$\frac{11 y}{11} < \frac{33}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 y}{11} < \frac{33}{11}$

Divide $y$ by $1$ .

$y < \frac{33}{11}$

Simplify the right side.

Divide $33$ by $11$ .

$y < 3$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$y < 3$

Interval Notation:

$(- \infty, 3)$