Question

Solve the following compound inequality:

−3(x + 7) − 15 > 2x + 4 or −2x + 6 < 4(x − 3)



a
x < −8 or x > 3

b
x > −8 or x < 3

c
x < 8 or x > −3

d
x > 8 or x < −3

Answer 1

Answer: a

Explanation:

`-3(x+7)-15 > 2x+4\\\\-3x-21-15 > 2x+4\\\\-3x-36 > 2x+4\\\\-36 > 5x+4\\\\-40 > 5x\\\\x < -8`

`-2x+6 < 4(x-3)\\\\-2x+6 < 4x-12\\\\6 < 6x-12\\\\18 < 6x\\\\x > 3`

Taking the union, we get that
`x < -8` or
`x > 3`.