Question

Solve (4 - x ≤ -1) ∩ (2 + 3x ≥ 17).

Answer 1

The upside down 'U' shape means intersection which means find the terms that are in both of the groups so  for example (2,4,6,7) (upside down U shape) (3,5,7) the answer would be (7) because 7 is in both of the sets
< means less than or equal to
> means more than or equal to
so so 4-x<-1
if we convert this to x=something then
add x to both sides
4<x-1
add 1 to both sides
5<x

the second equation is 2+3x> 17
subtract 2 from both sides
3x>15
divide both sides by 3
x>5

so the intersection of 5<x and x>5 is 5<x>5 or 5<x so the solution set is x={x|x>5} or any number more than or equal to 5 will work

Answer 2

$4-x \leq -1\ \ \ | subtract\ 4\ \ \ \ \ and\ \ \ \ 2+3x \geq 17\ \ \ | subtract\ 2\\\\ -x \leq -5\ |*(-1)\ \ \ \ and\ \ \ \ 3x \geq 15\ \ | divide\ by\ 3\\\\ x \geq 5\ \ \ \ \ and\ \ \ \ x \geq 5\\\\ Solution\ is\ x\in[5,+\infty)$