Solve the System of Inequalities 38<-5x-7 or -57<-5x-7

$38 < - 5 x - 7$ or $- 57 < - 5 x - 7$

Step 1

Simplify the first inequality.

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

$- 5 x - 7 > 38$ or $- 57 < - 5 x - 7$

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

Add $7$ to both sides of the inequality.

$- 5 x > 38 + 7$ or $- 57 < - 5 x - 7$

Add $38$ and $7$ .

$- 5 x > 45$ or $- 57 < - 5 x - 7$

Divide each term in $- 5 x > 45$ by $- 5$ and simplify.

Divide each term in $- 5 x > 45$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} < \frac{45}{- 5}$ or $- 57 < - 5 x - 7$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} < \frac{45}{- 5}$ or $- 57 < - 5 x - 7$

Divide $x$ by $1$ .

$x < \frac{45}{- 5}$ or $- 57 < - 5 x - 7$

Simplify the right side.

Divide $45$ by $- 5$ .

$x < - 9$ or $- 57 < - 5 x - 7$

Step 2

Simplify the second inequality.

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

$x < - 9$ or $- 5 x - 7 > - 57$

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

Add $7$ to both sides of the inequality.

$x < - 9$ or $- 5 x > - 57 + 7$

Add $- 57$ and $7$ .

$x < - 9$ or $- 5 x > - 50$

Divide each term in $- 5 x > - 50$ by $- 5$ and simplify.

Divide each term in $- 5 x > - 50$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < - 9$ or $\frac{- 5 x}{- 5} < \frac{- 50}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$x < - 9$ or $\frac{- 5 x}{- 5} < \frac{- 50}{- 5}$

Divide $x$ by $1$ .

$x < - 9$ or $x < \frac{- 50}{- 5}$

Simplify the right side.

Divide $- 50$ by $- 5$ .

$x < - 9$ or $x < 10$

Step 3

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

$x < 10$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 10$

Interval Notation:

$(- \infty, 10)$

Step 5

Solve the System of Inequalities 38<-5x-7 or -57<-5x-7

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