Solve for y 2(y+1)<3(y-8)

$2 (y + 1) < 3 (y - 8)$

Step 1

Simplify $2 (y + 1)$ .

Rewrite.

$0 + 0 + 2 (y + 1) < 3 (y - 8)$

Simplify by adding zeros.

$2 (y + 1) < 3 (y - 8)$

Apply the distributive property.

$2 y + 2 \cdot 1 < 3 (y - 8)$

Multiply $2$ by $1$ .

$2 y + 2 < 3 (y - 8)$

Step 2

Simplify $3 (y - 8)$ .

Apply the distributive property.

$2 y + 2 < 3 y + 3 \cdot - 8$

Multiply $3$ by $- 8$ .

$2 y + 2 < 3 y - 24$

Step 3

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

Subtract $3 y$ from both sides of the inequality.

$2 y + 2 - 3 y < - 24$

Subtract $3 y$ from $2 y$ .

$- y + 2 < - 24$

Step 4

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

Subtract $2$ from both sides of the inequality.

$- y < - 24 - 2$

Subtract $2$ from $- 24$ .

$- y < - 26$

Step 5

Divide each term in $- y < - 26$ by $- 1$ and simplify.

Divide each term in $- y < - 26$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{- 26}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{- 26}{- 1}$

Divide $y$ by $1$ .

$y > \frac{- 26}{- 1}$

Simplify the right side.

Divide $- 26$ by $- 1$ .

$y > 26$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$y > 26$

Interval Notation:

$(26, \infty)$

Solve for y 2(y+1)<3(y-8)

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