Question

How do you solve `5v + 10<= - 4v - 17< 9- 2v`?

Answer 1

`-13 < v <=- 3`

Explanation:

Break the inequality into 2 parts and solve each separately.

`color(blue)(5v +10 <= -4v -17) < 9-2v`
`5v +10 <= color(red)(-4v -17 < 9-2v)`

`color(blue)(5v +10 <= -4v -17)`
`color(blue)(10+17 <= -4v-5v)`
`color(blue)(27<=-9v)" "div -9" "larr` change sign around
`color(blue)(-3 >=v)`

`color(red)(-4v -17 < 9-2v)`
`color(red)(-17 -9 <-2v+4v)`
`color(red)(-26 <2v)`
`color(red)(-13 < v)`

Combine the two solutions for v:
`color(red)(-13 < v)" and "color(blue)(v<=-3)`

`color(red)(-13 <) v color(blue)(<= -3)`