Question

Please help ASAP!

What is the solution to the compound inequality in interval notation?
2(2x−1)>6  or  x+3≤−6

A). (−∞, −9) or [2, ∞)
B). (−∞, −9] or (2, ∞)
C). [−9, 2)
D). (−∞, −9) or (2, ∞)

Answer 1

It is given in the question that

`2(2x-1)>6 \ or \ x+3 \leq -6`

For th first inequality, we divide both sides by 2, and for second, we subtract 3 to both sides, that is

`2x-1>3 \ or \ x \leq -6-3 \\ 2x>4 \ or \ x \leq -9 \\ x>2 \ or \ x \leq -9`

So the required inequality is

`(- \infty, -9] U (2, \infty)`

Correct option is B