Solve the System of Inequalities 20>-3x-7 and -28>=-3x-7

$20 > - 3 x - 7$ and $- 28 \geq - 3 x - 7$

Step 1

Simplify the first inequality.

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

$- 3 x - 7 < 20$ and $- 28 \geq - 3 x - 7$

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

Add $7$ to both sides of the inequality.

$- 3 x < 20 + 7$ and $- 28 \geq - 3 x - 7$

Add $20$ and $7$ .

$- 3 x < 27$ and $- 28 \geq - 3 x - 7$

Divide each term in $- 3 x < 27$ by $- 3$ and simplify.

Divide each term in $- 3 x < 27$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{27}{- 3}$ and $- 28 \geq - 3 x - 7$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{27}{- 3}$ and $- 28 \geq - 3 x - 7$

Divide $x$ by $1$ .

$x > \frac{27}{- 3}$ and $- 28 \geq - 3 x - 7$

Simplify the right side.

Divide $27$ by $- 3$ .

$x > - 9$ and $- 28 \geq - 3 x - 7$

Step 2

Simplify the second inequality.

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

$x > - 9$ and $- 3 x - 7 \leq - 28$

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

Add $7$ to both sides of the inequality.

$x > - 9$ and $- 3 x \leq - 28 + 7$

Add $- 28$ and $7$ .

$x > - 9$ and $- 3 x \leq - 21$

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.

$x > - 9$ and $\frac{- 3 x}{- 3} \geq \frac{- 21}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$x > - 9$ and $\frac{- 3 x}{- 3} \geq \frac{- 21}{- 3}$

Divide $x$ by $1$ .

$x > - 9$ and $x \geq \frac{- 21}{- 3}$

Simplify the right side.

Divide $- 21$ by $- 3$ .

$x > - 9$ and $x \geq 7$

Step 3

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

$x \geq 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 7$

Interval Notation:

$[7, \infty)$

Step 5

Solve the System of Inequalities 20>-3x-7 and -28>=-3x-7

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