Question

How do I solve the polynomial inequality `-6<=2(x-5)<7`?

Answer 1

`2<=x<17/2`

Explanation:

(1)`-6<=2(x-5)` and (2)`2(x-5)<7`

(1):
`-6<=2 x-10`
`10-6<=2x`
`4<=2x`
`2 <=x`

(2)
`2(x-5)<7`
`2 x-10<7`
`2 x < 7+10`
`2 x <17`
`x<17/2`

Result:
`2<=x<17/2`