Question

How do you solve the graph: 1<3x-2≤10?

Answer 1

`1 < x <= 4`
as a line graph:

Explanation:

Given an inequality, you can
- add the same amount to both sides
- divide both sides by any amount greater than zero
without effecting the validity or orientation of the inequality

`1 < 3x-2 <=10`

can be split into two inequalities

`1 < 3x-2`
`color(white)("XXX")rarr 3 < 3x`
`color(white)("XXX")rarr 1 < x`

and

`3x-2 <= 10`
`color(white)("XXX")rarr 3x <= 12`
`color(white)("XXX")rarr x <= 4`