Solve for v 5/6v+7<=-3

$\frac{5}{6} v + 7 \leq - 3$

Step 1

Combine $\frac{5}{6}$ and $v$ .

$\frac{5 v}{6} + 7 \leq - 3$

Step 2

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

Subtract $7$ from both sides of the inequality.

$\frac{5 v}{6} \leq - 3 - 7$

Subtract $7$ from $- 3$ .

$\frac{5 v}{6} \leq - 10$

Step 3

Multiply both sides by $6$ .

$\frac{5 v}{6} \cdot 6 \leq - 10 \cdot 6$

Step 4

Simplify.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{5 v}{6} \cdot 6 \leq - 10 \cdot 6$

Rewrite the expression.

$5 v \leq - 10 \cdot 6$

Simplify the right side.

Multiply $- 10$ by $6$ .

$5 v \leq - 60$

Step 5

Divide each term in $5 v \leq - 60$ by $5$ and simplify.

Divide each term in $5 v \leq - 60$ by $5$ .

$\frac{5 v}{5} \leq \frac{- 60}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 v}{5} \leq \frac{- 60}{5}$

Divide $v$ by $1$ .

$v \leq \frac{- 60}{5}$

Simplify the right side.

Divide $- 60$ by $5$ .

$v \leq - 12$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$v \leq - 12$

Interval Notation:

$(- \infty, - 12]$