Solve the System of Inequalities -20>-5x-10 and -5x-10>=-70

$- 20 > - 5 x - 10$ and $- 5 x - 10 \geq - 70$

Step 1

Simplify the first inequality.

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

$- 5 x - 10 < - 20$ and $- 5 x - 10 \geq - 70$

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

Add $10$ to both sides of the inequality.

$- 5 x < - 20 + 10$ and $- 5 x - 10 \geq - 70$

Add $- 20$ and $10$ .

$- 5 x < - 10$ and $- 5 x - 10 \geq - 70$

Divide each term in $- 5 x < - 10$ by $- 5$ and simplify.

Divide each term in $- 5 x < - 10$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} > \frac{- 10}{- 5}$ and $- 5 x - 10 \geq - 70$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} > \frac{- 10}{- 5}$ and $- 5 x - 10 \geq - 70$

Divide $x$ by $1$ .

$x > \frac{- 10}{- 5}$ and $- 5 x - 10 \geq - 70$

Simplify the right side.

Divide $- 10$ by $- 5$ .

$x > 2$ and $- 5 x - 10 \geq - 70$

Step 2

Simplify the second inequality.

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

Add $10$ to both sides of the inequality.

$x > 2$ and $- 5 x \geq - 70 + 10$

Add $- 70$ and $10$ .

$x > 2$ and $- 5 x \geq - 60$

Divide each term in $- 5 x \geq - 60$ by $- 5$ and simplify.

Divide each term in $- 5 x \geq - 60$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x > 2$ and $\frac{- 5 x}{- 5} \leq \frac{- 60}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$x > 2$ and $\frac{- 5 x}{- 5} \leq \frac{- 60}{- 5}$

Divide $x$ by $1$ .

$x > 2$ and $x \leq \frac{- 60}{- 5}$

Simplify the right side.

Divide $- 60$ by $- 5$ .

$x > 2$ and $x \leq 12$

Step 3

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

$2 < x \leq 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$2 < x \leq 12$

Interval Notation:

$(2, 12]$

Step 5

Solve the System of Inequalities -20>-5x-10 and -5x-10>=-70

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