IMAT 2012 Q70 [Inequalities]

What is the set of values of x for which {x^2<9} and {2x + 3\ge 5} ?

A. x>3
B. x\ge -1
C. 1 \le x <3
D. x< -3 or x\ge 1
E. x> -3

Let’s break down each inequality:

If x^2 < 9 then x^2 -9 < 0, and (x+3)(x-3) < 0

So, -3 < x < 3

If 2x+3 \ge 5 then 2x \ge 2 and so x \ge 1

We need to find what will satisfy both statements, -3 < x < 3 and x \ge 1

Using the wavy method or a simple number line, we know that x > -3 becomes irrelevant, and we are left with a simple satisfaction of 3 > x \ge 1.

Making our answer C.