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Last Updated on May 4, 2023
GMAT OFFICIAL GUIDE PS
Solution:
To solve, we first isolate the x^2 in the inequality 1 – x^2 ≥ 0. So we have:
1 ≥ x^2
Next, we take the square root of both sides, to isolate x.
√1 ≥ √x^2
This gives us:
1 ≥ |x|
Because the variable x is inside the absolute value sign, we must consider that x can be either positive or negative. Therefore, we’ll need to solve the inequality twice.
When x is positive:
1 ≥ |x| means
1 ≥ x
This can be re-expressed as x ≤ 1.
When x is negative:
1 ≥ |x| means
1 ≥ -x (Divide both sides by -1 and switch the inequality sign)
-1 ≤ x
We combine the two resulting inequalities to get:
-1 ≤ x ≤ 1
Answer: E
