Question

How do you solve `-11< 2x - 1\leq 7`?

Answer 1

`-5< x <=4`

Explanation:

`"add 1 to each of the 3 intervals"`

`-11color(red)(+1)<2xcancel(-1)cancel(color(red)(+1))<=7color(red)(+1)`

`-10<2x<=8`

`"divide each interval by 2"`

`-5< x<=4`

`x in(-5,4]larrcolor(blue)"in interval notation"`

Answer 2

`-5< x<=4`

Explanation:

We can start by adding `1` to all three parts of this inequality. We get

`-10<2x<=8`

Lastly, we can divide all three parts by `2` to isolate `x`. We get

`bar(ul(|color(white)(2/2)(-5< x<=4)color(white)(2/2)|`

The key realization here is that we have three parts to the inequality, so we have to apply the operations to all three parts of it.

Hope this helps!