Question

How do you solve and write the following in interval notation: `2x − 1 < x + 6 <3x − 4`?

Answer 1

`7 > x > 5`

Explanation:

`2x - 1 < x + 6 < 3x - 4`

We will divide the equations into two parts!

`2x - 1 < x + 6 and x + 6 < 3x - 4`

Solving the First Part!

`2x - 1 < x + 6`

Subtract `x` from both sides..

`2x - 1 - x < x + 6 - x`

`2x - x - 1 < x - x + 6`

`x - 1 < 0 + 6`

`x - 1 < 6`

Add `1` to both sides

`x - 1 + 1 < 6 + 1`

`x + 0 < 7`

`x < 7`

Same as `7 > x`

Solving the Second Part!

`x + 6 < 3x - 4`

Subtract `x` from both sides..

`x + 6 - x < 3x - 4 - x`

`x - x + 6 < 3x - x - 4`

`0 + 6 < 2x - 4`

`6 < 2x - 4`

Add `4` to both sides..

`6 + 4 < 2x - 4 + 4`

`10 < 2x + 0`

`10 <2x`

Divide both sides by `2`

`10/2 < (2x)/2`

`10/2 < (cancel2x)/cancel2`

`10/2 < x`

`5 < x`

Same as `x > 5`

Hence adding both..

`7 > x > 5`