Solve the System of Inequalities 7v-5>=65 or -3v-2>=-2

$7 v - 5 \geq 65$ or $- 3 v - 2 \geq - 2$

Step 1

Simplify the first inequality.

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

Add $5$ to both sides of the inequality.

$7 v \geq 65 + 5$

Add $65$ and $5$ .

$7 v \geq 70$

Divide each term in $7 v \geq 70$ by $7$ and simplify.

Divide each term in $7 v \geq 70$ by $7$ .

$\frac{7 v}{7} \geq \frac{70}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 v}{7} \geq \frac{70}{7}$

Divide $v$ by $1$ .

$v \geq \frac{70}{7}$

Simplify the right side.

Divide $70$ by $7$ .

$v \geq 10$

Step 2

Simplify the second inequality.

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

Add $2$ to both sides of the inequality.

$- 3 v \geq - 2 + 2$

Add $- 2$ and $2$ .

$- 3 v \geq 0$

Divide each term in $- 3 v \geq 0$ by $- 3$ and simplify.

Divide each term in $- 3 v \geq 0$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 v}{- 3} \leq \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 v}{- 3} \leq \frac{0}{- 3}$

Divide $v$ by $1$ .

$v \leq \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

$v \leq 0$

Step 3

The union consists of all of the elements that are contained in each interval.

$v \leq 0$ or $v \geq 10$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$v \leq 0 or v \geq 10$

Interval Notation:

$(- \infty, 0] \cup [10, \infty)$

Step 5

Solve the System of Inequalities 7v-5>=65 or -3v-2>=-2

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