Question

Solve the compound inequality.
x+3<0 or 5x>−10

Answer 1

`x + 3 < 0 \: \: or \: \: 5x > - 10 \\ \\ x < - 3 \: \: or \: \: x > - 2 \\ \\ { \boxed{ \: \: - 3 < x < - 2 \: \: }}`

Answer 2

x < – 3 or x > – 2

Explanation:

For x + 3 < 0 :

subtract 3 from both sides of the inequality:

x + 3 – 3 < 0 – 3

x + 0 < – 3

x < –3

For 5x > – 10:

Divide both sides of the inequality by 5 to isolate x:

`(5x)/(5) > (-10)/(5)`

x > –2

Therefore:

x < – 3 or x > –2

Interval notation: [(– ∞, –3) ∪ (–2, ∞)]