Solve the System of Inequalities -3x-6<=3 or -3x-6<-21

$- 3 x - 6 \leq 3$ or $- 3 x - 6 < - 21$

Step 1

Simplify the first inequality.

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

Add $6$ to both sides of the inequality.

$- 3 x \leq 3 + 6$ or $- 3 x - 6 < - 21$

Add $3$ and $6$ .

$- 3 x \leq 9$ or $- 3 x - 6 < - 21$

Divide each term in $- 3 x \leq 9$ by $- 3$ and simplify.

Divide each term in $- 3 x \leq 9$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \geq \frac{9}{- 3}$ or $- 3 x - 6 < - 21$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{9}{- 3}$ or $- 3 x - 6 < - 21$

Divide $x$ by $1$ .

$x \geq \frac{9}{- 3}$ or $- 3 x - 6 < - 21$

Simplify the right side.

Divide $9$ by $- 3$ .

$x \geq - 3$ or $- 3 x - 6 < - 21$

Step 2

Simplify the second inequality.

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

Add $6$ to both sides of the inequality.

$x \geq - 3$ or $- 3 x < - 21 + 6$

Add $- 21$ and $6$ .

$x \geq - 3$ or $- 3 x < - 15$

Divide each term in $- 3 x < - 15$ by $- 3$ and simplify.

Divide each term in $- 3 x < - 15$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x \geq - 3$ or $\frac{- 3 x}{- 3} > \frac{- 15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$x \geq - 3$ or $\frac{- 3 x}{- 3} > \frac{- 15}{- 3}$

Divide $x$ by $1$ .

$x \geq - 3$ or $x > \frac{- 15}{- 3}$

Simplify the right side.

Divide $- 15$ by $- 3$ .

$x \geq - 3$ or $x > 5$

Step 3

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

$x \geq - 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 3$

Interval Notation:

$[- 3, \infty)$

Step 5

Solve the System of Inequalities -3x-6<=3 or -3x-6<-21

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