Solve the System of Inequalities x+2<-4 or -5x<-15

$x + 2 < - 4$ or $- 5 x < - 15$

Step 1

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

Subtract $2$ from both sides of the inequality.

$x < - 4 - 2$ or $- 5 x < - 15$

Subtract $2$ from $- 4$ .

$x < - 6$ or $- 5 x < - 15$

Step 2

Divide each term in $- 5 x < - 15$ by $- 5$ and simplify.

Divide each term in $- 5 x < - 15$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x < - 6$ or $\frac{- 5 x}{- 5} > \frac{- 15}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$x < - 6$ or $\frac{- 5 x}{- 5} > \frac{- 15}{- 5}$

Divide $x$ by $1$ .

$x < - 6$ or $x > \frac{- 15}{- 5}$

Simplify the right side.

Divide $- 15$ by $- 5$ .

$x < - 6$ or $x > 3$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x < - 6 or x > 3$

Interval Notation:

$(- \infty, - 6) \cup (3, \infty)$

Step 4

Solve the System of Inequalities x+2<-4 or -5x<-15

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