Solve the System of Inequalities v+8<3 or -8v<-40

$v + 8 < 3$ or $- 8 v < - 40$

Step 1

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

Subtract $8$ from both sides of the inequality.

$v < 3 - 8$ or $- 8 v < - 40$

Subtract $8$ from $3$ .

$v < - 5$ or $- 8 v < - 40$

Step 2

Divide each term in $- 8 v < - 40$ by $- 8$ and simplify.

Divide each term in $- 8 v < - 40$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$v < - 5$ or $\frac{- 8 v}{- 8} > \frac{- 40}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$v < - 5$ or $\frac{- 8 v}{- 8} > \frac{- 40}{- 8}$

Divide $v$ by $1$ .

$v < - 5$ or $v > \frac{- 40}{- 8}$

Simplify the right side.

Divide $- 40$ by $- 8$ .

$v < - 5$ or $v > 5$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$v < - 5 or v > 5$

Interval Notation:

$(- \infty, - 5) \cup (5, \infty)$

Step 4

Solve the System of Inequalities v+8<3 or -8v<-40

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