Solve the System of Inequalities -3x-7<=11 and -10<-3x-7

$- 3 x - 7 \leq 11$ and $- 10 < - 3 x - 7$

Step 1

Simplify the first inequality.

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

Add $7$ to both sides of the inequality.

$- 3 x \leq 11 + 7$ and $- 10 < - 3 x - 7$

Add $11$ and $7$ .

$- 3 x \leq 18$ and $- 10 < - 3 x - 7$

Divide each term in $- 3 x \leq 18$ by $- 3$ and simplify.

Divide each term in $- 3 x \leq 18$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \geq \frac{18}{- 3}$ and $- 10 < - 3 x - 7$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{18}{- 3}$ and $- 10 < - 3 x - 7$

Divide $x$ by $1$ .

$x \geq \frac{18}{- 3}$ and $- 10 < - 3 x - 7$

Simplify the right side.

Divide $18$ by $- 3$ .

$x \geq - 6$ and $- 10 < - 3 x - 7$

Step 2

Simplify the second inequality.

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

$x \geq - 6$ and $- 3 x - 7 > - 10$

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

Add $7$ to both sides of the inequality.

$x \geq - 6$ and $- 3 x > - 10 + 7$

Add $- 10$ and $7$ .

$x \geq - 6$ and $- 3 x > - 3$

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

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

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 3$ by $- 3$ .

$x \geq - 6$ and $x < 1$

Step 3

The intersection consists of the elements that are contained in both intervals.

$- 6 \leq x < 1$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 6 \leq x < 1$

Interval Notation:

$[- 6, 1)$

Step 5

Solve the System of Inequalities -3x-7<=11 and -10<-3x-7

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