Solve the Inequality for y 9y+5(y+3)<4y-35

$9 y + 5 (y + 3) < 4 y - 35$

Step 1

Simplify $9 y + 5 (y + 3)$ .

Simplify each term.

Apply the distributive property.

$9 y + 5 y + 5 \cdot 3 < 4 y - 35$

Multiply $5$ by $3$ .

$9 y + 5 y + 15 < 4 y - 35$

Add $9 y$ and $5 y$ .

$14 y + 15 < 4 y - 35$

Step 2

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

Subtract $4 y$ from both sides of the inequality.

$14 y + 15 - 4 y < - 35$

Subtract $4 y$ from $14 y$ .

$10 y + 15 < - 35$

Step 3

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

Subtract $15$ from both sides of the inequality.

$10 y < - 35 - 15$

Subtract $15$ from $- 35$ .

$10 y < - 50$

Step 4

Divide each term in $10 y < - 50$ by $10$ and simplify.

Divide each term in $10 y < - 50$ by $10$ .

$\frac{10 y}{10} < \frac{- 50}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} < \frac{- 50}{10}$

Divide $y$ by $1$ .

$y < \frac{- 50}{10}$

Simplify the right side.

Divide $- 50$ by $10$ .

$y < - 5$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$y < - 5$

Interval Notation:

$(- \infty, - 5)$