Solve the System of Inequalities -3x-10<=11 and -34<-3x-10

$- 3 x - 10 \leq 11$ and $- 34 < - 3 x - 10$

Step 1

Simplify the first inequality.

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

Add $10$ to both sides of the inequality.

$- 3 x \leq 11 + 10$ and $- 34 < - 3 x - 10$

Add $11$ and $10$ .

$- 3 x \leq 21$ and $- 34 < - 3 x - 10$

Divide each term in $- 3 x \leq 21$ by $- 3$ and simplify.

Divide each term in $- 3 x \leq 21$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} \geq \frac{21}{- 3}$ and $- 34 < - 3 x - 10$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{21}{- 3}$ and $- 34 < - 3 x - 10$

Divide $x$ by $1$ .

$x \geq \frac{21}{- 3}$ and $- 34 < - 3 x - 10$

Simplify the right side.

Divide $21$ by $- 3$ .

$x \geq - 7$ and $- 34 < - 3 x - 10$

Step 2

Simplify the second inequality.

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

$x \geq - 7$ and $- 3 x - 10 > - 34$

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

Add $10$ to both sides of the inequality.

$x \geq - 7$ and $- 3 x > - 34 + 10$

Add $- 34$ and $10$ .

$x \geq - 7$ and $- 3 x > - 24$

Divide each term in $- 3 x > - 24$ by $- 3$ and simplify.

Divide each term in $- 3 x > - 24$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x \geq - 7$ and $\frac{- 3 x}{- 3} < \frac{- 24}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$x \geq - 7$ and $\frac{- 3 x}{- 3} < \frac{- 24}{- 3}$

Divide $x$ by $1$ .

$x \geq - 7$ and $x < \frac{- 24}{- 3}$

Simplify the right side.

Divide $- 24$ by $- 3$ .

$x \geq - 7$ and $x < 8$

Step 3

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

$- 7 \leq x < 8$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 7 \leq x < 8$

Interval Notation:

$[- 7, 8)$

Step 5

Solve the System of Inequalities -3x-10<=11 and -34<-3x-10

Related Questions

Support LCMGCF.com by disabling your adblocker.