Question

How do you solve and write the following in interval notation: `abs(3(x+2)-7x)<=6`?

Answer 1

`0<=x<=3`

Explanation:

`∣3x+6-7x∣<=6`
`∣6-4x∣<=6`
`6-4x<=6` and `-(6-4x)<=6`
`-4x<=0` and `-6+4x<=6`
`4x>=0` and `4x<=12`
`x>=0` and `x<=3`
the answer is `0<=x<=3`
Checking, let `x=2`
LHS `6-4*2=-2` and `∣-2∣=2`
RHS `=6`
so `2` is `<=6`