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.
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