Question

Solve the following inequalities and give the solutions in both set and interval notations.

1 < 4x + 2 < 10

Answer 1

1<4x+2<10

= -1/4<x<2

x=(-1/4,2)

Answer 2

`1 < 4x + 2 < 10`

First let's subtract 2 from everything in the inequality:

`1 - 2 < 4x + 2 - 2 < 10 - 2`

`-1 < 4x < 8`

Next, let's divide 4 from everything in the inequality:

`(-1)/(4) < (4x)/(4) < (8)/(4)`

`(-1)/(4) < x < 2`

This is the final solution to the inequality:
`((-1)/(4), 2)`