Question

How do you solve `2x^3-6x^2+x-1<=2x-3?`

Answer 1

Firstly set it `=` to `0` by taking away `2x-3` from both sides.
This leaves us with:
`2x^3 - 6x^2 - x +2 <= 0`
Then we can use the factor theorem to find one of our roots.
Start with `f(x) = 1`
`2(1)^3 -6(1)^2 -(1) +2 = -3` Not a factor
Try `2`
`2(2)^3 -6(2)^2 -(2) +2 = -8` Not a factor
Try `-1`
`2(-1)^3 -6(-1)^2 -(-1) +2 = -7` Not a factor
Try `-2`
`2(-2)^3 -6(-2)^2 -(-2) +2 = -36` Not a factor
Try `3`
`2(3)^3 -6(3)^2 -(3) +2 = -1` Not a factor
Try `4`
`2(4)^3 -6(4)^2 -(4) +2 = 30` Not a factor.

Very sorry I think I've done something wrong but I thought I'd send you my working a)because I find sometimes reading what someone else has done, even if wrong, helps to solve things and b)because I cant bring myself to get rid of that working.

It could be possible that you just need a factor higher than I'm using so feel free to try some, and if so you'll need to do some algebraic long division. Happy to show you this if you find a factor!