Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We must determine all of the values of x based on the inequality x^2 – 2 < 0. To determine all the possible values of x, let’s simplify the inequality.
x^2 < 2
√x^2 < √2
|x| < √2
Note that when we take the square root of x^2, the value of x itself can be either negative or positive, and thus we express this as |x|, the absolute value of x.
Remember also that when we are solving an absolute value equation or inequality, we consider two cases: when the quantity inside the absolute value is positive and then when the quantity inside the absolute value is negative.
Let’s now solve for when x is positive and then for when x is negative.
When x is positive
x < √2
When x is negative
-x < √2
x > -√2
Combining these two inequalities, we have:
-√2 < x < √2
Answer: C
