Solve the System of Inequalities 3x+5>=-1 or -2x-7>=5

$3 x + 5 \geq - 1$ or $- 2 x - 7 \geq 5$

Step 1

Simplify the first inequality.

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

Subtract $5$ from both sides of the inequality.

$3 x \geq - 1 - 5$

Subtract $5$ from $- 1$ .

$3 x \geq - 6$

Divide each term in $3 x \geq - 6$ by $3$ and simplify.

Divide each term in $3 x \geq - 6$ by $3$ .

$\frac{3 x}{3} \geq \frac{- 6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{- 6}{3}$

Divide $x$ by $1$ .

$x \geq \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

$x \geq - 2$

Step 2

Simplify the second inequality.

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

Add $7$ to both sides of the inequality.

$- 2 x \geq 5 + 7$

Add $5$ and $7$ .

$- 2 x \geq 12$

Divide each term in $- 2 x \geq 12$ by $- 2$ and simplify.

Divide each term in $- 2 x \geq 12$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} \leq \frac{12}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} \leq \frac{12}{- 2}$

Divide $x$ by $1$ .

$x \leq \frac{12}{- 2}$

Simplify the right side.

Divide $12$ by $- 2$ .

$x \leq - 6$

Step 3

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

$x \leq - 6$ or $x \geq - 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 6 or x \geq - 2$

Interval Notation:

$(- \infty, - 6] \cup [- 2, \infty)$

Step 5

Solve the System of Inequalities 3x+5>=-1 or -2x-7>=5

Related Questions

Support LCMGCF.com by disabling your adblocker.