What interval consists of all $w$ which satisfy ${\bf neither}$ $-2(6+2w)\le -16$ nor $-3w\ge 18$ ?
+9466 What interval consists of all \(w\) which satisfy \(\bf neither\) \(-2(6+2w)\le -16\) nor \(-3w\ge 18\) ?
If w makes the inequality -2(6 + 2w) ≤ -16 false, then
it must make the inequality -2(6 + 2w) > -16 true.
-2(6 + 2w) > -16
Divide both sides by -2, a negative number, so flip the sign
6 + 2w < 8
Subtract 6 from both sides of the inequality.
2w < 2
Divide both sides by 2, a positive number, so don't flip the sign
w < 1
If -2(6 + 2w) > -16 then w < 1
If w makes the inequality -3w ≥ 18 false, then
it must make the inequality -3w < 18 true.
-3w < 18
Divide both sides by 3, a negative number, so flip the sign.
w > -6
If -3w < 18 then w > -6
So the solution to the question is all w such that w < 1 and w > -6
That is all w in the interval (-6, 1)
