Range of Values For Inequalities

[kc1895]

Here is a basic inequality question for which I cannot understand the answer:

If \(\displaystyle -1<a-b<10 ,and -3\le b\le1\) then what inequality represents the range of values of a²?

I plug-in -3 and 1 for b for boundaries and get -4<a<11.
Since the boundary is for a², the range would be 16<a²<121.

But why would this be incorrect?

Thanks for your help!

 

[MarkFL]

Given that:

\(\displaystyle -4<a<11\)

this implies:

\(\displaystyle 0\le|a|<11\)

Now, using:

\(\displaystyle |x|\equiv\sqrt{x^2}\)

we may write:

\(\displaystyle 0\le\sqrt{a^2}<11\)

And so squaring through the compound inequality, we obtain:

\(\displaystyle 0\le a^2<121\)