Solve the Inequality for s 3s+6<=-5(s+2)

$3 s + 6 \leq - 5 (s + 2)$

Step 1

Simplify $- 5 (s + 2)$ .

Rewrite.

$3 s + 6 \leq 0 + 0 - 5 (s + 2)$

Simplify by adding zeros.

$3 s + 6 \leq - 5 (s + 2)$

Apply the distributive property.

$3 s + 6 \leq - 5 s - 5 \cdot 2$

Multiply $- 5$ by $2$ .

$3 s + 6 \leq - 5 s - 10$

Step 2

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

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

$3 s + 6 + 5 s \leq - 10$

Add $3 s$ and $5 s$ .

$8 s + 6 \leq - 10$

Step 3

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

Subtract $6$ from both sides of the inequality.

$8 s \leq - 10 - 6$

Subtract $6$ from $- 10$ .

$8 s \leq - 16$

Step 4

Divide each term in $8 s \leq - 16$ by $8$ and simplify.

Divide each term in $8 s \leq - 16$ by $8$ .

$\frac{8 s}{8} \leq \frac{- 16}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 s}{8} \leq \frac{- 16}{8}$

Divide $s$ by $1$ .

$s \leq \frac{- 16}{8}$

Simplify the right side.

Divide $- 16$ by $8$ .

$s \leq - 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$s \leq - 2$

Interval Notation:

$(- \infty, - 2]$