Solve for v -9>-2-3/4v

$- 9 > - 2 - \frac{3}{4} v$

Step 1

Rewrite so $v$ is on the left side of the inequality.

$- 2 - \frac{3}{4} v < - 9$

Step 2

Simplify each term.

Combine $v$ and $\frac{3}{4}$ .

$- 2 - \frac{v \cdot 3}{4} < - 9$

Move $3$ to the left of $v$ .

$- 2 - \frac{3 v}{4} < - 9$

Step 3

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

Add $2$ to both sides of the inequality.

$- \frac{3 v}{4} < - 9 + 2$

Add $- 9$ and $2$ .

$- \frac{3 v}{4} < - 7$

Step 4

Divide each term in $- \frac{3 v}{4} < - 7$ by $- 1$ and simplify.

Divide each term in $- \frac{3 v}{4} < - 7$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{3 v}{4}}{- 1} > \frac{- 7}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{\frac{3 v}{4}}{1} > \frac{- 7}{- 1}$

Divide $\frac{3 v}{4}$ by $1$ .

$\frac{3 v}{4} > \frac{- 7}{- 1}$

Simplify the right side.

Divide $- 7$ by $- 1$ .

$\frac{3 v}{4} > 7$

Step 5

Multiply both sides by $4$ .

$\frac{3 v}{4} \cdot 4 > 7 \cdot 4$

Step 6

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 v}{4} \cdot 4 > 7 \cdot 4$

Rewrite the expression.

$3 v > 7 \cdot 4$

Simplify the right side.

Multiply $7$ by $4$ .

$3 v > 28$

Step 7

Divide each term in $3 v > 28$ by $3$ and simplify.

Divide each term in $3 v > 28$ by $3$ .

$\frac{3 v}{3} > \frac{28}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 v}{3} > \frac{28}{3}$

Divide $v$ by $1$ .

$v > \frac{28}{3}$

Step 8

The result can be shown in multiple forms.

Inequality Form:

$v > \frac{28}{3}$

Interval Notation:

$(\frac{28}{3}, \infty)$

Solve for v -9>-2-3/4v

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