1 - x^2 ≥ 0
Simplify as, (1-x)(1+x) ≥ 0

this tells x≥-1 & x<=1

Seeing the options down, you can eliminate A, B as they satisfy only one condition
Eliminate D as it is exactly opposite to the condition
Eliminate C, as this condition is only upto 0 and not -1

So, finally E is the right choice that satisfies

This problem is best and fast to factorize than plugging in numbers

kishokbabu wrote:173. Which of the following describes all values of x for
which 1 - x^2 ≥ 0 ?

(A) x ≥ 1
(B) x ≤ -1
(C) 0 ≤ x ≤ 1
(D) x ≤ -1 or x ≥ 1
(E) -1 ≤ x ≤ 1

Kindly help me to solve this problem with some plugging the number option or any better approach

Its known that the square value between 0 and +1 is less than 1 eg 1/2^2=1/4
and the same is for 0 to -1 eg -1/2^2=1/4
values other than this have values greater than 1
and in the Q we have to find all values for which 1-x^2>=0
so x^2 should not be greater than 1 at max value X^2 can have is 1.
1-x^2 will be >=0 when
-1<=X<=1

kishokbabu wrote:173. Which of the following describes all values of x for
which 1 - x^2 ≥ 0 ?

(A) x ≥ 1
(B) x ≤ -1
(C) 0 ≤ x ≤ 1
(D) x ≤ -1 or x ≥ 1
(E) -1 ≤ x ≤ 1

Kindly help me to solve this problem with some plugging the number option or any better approach

It is possible that x = 1/2, since 1 - (1/2)² ≥ 0.
Eliminate any answer choice in which x = 1/2 does not work.
Eliminate A (since 1/2 ≥ 1 doesn't work), B (since 1/2 ≤ -1 doesn't work), and D (since neither 1/2 ≤ -1 nor 1/2 ≥ 1 works).

The only difference between C and E is that E includes values between -1 and 0.
It is possible that x = -1/2, since 1 - (-1/2)² ≥ 0.
Eliminate C, since it does not include x = -1/2 within its range.

The correct answer is E.

kishokbabu wrote:173. Which of the following describes all values of x for
which 1 - x^2 ≥ 0 ?

(A) x ≥ 1
(B) x ≤ -1
(C) 0 ≤ x ≤ 1
(D) x ≤ -1 or x ≥ 1
(E) -1 ≤ x ≤ 1

Kindly help me to solve this problem with some plugging the number option or any better approach

The equation can be rewritten as:
(x^2-1) <= 0
Which can be simplified as:
(x-1)(x+1)<=0

An easy way to solve such inequalities is to draw the roots on a number line and check in the regions on the left and right of the roots.
The roots are 1 and -1. Hence, we need to check for x > 1, -1 <= x <= 1, x < -1; wherever (x^2 - 1)<=0, that region is a solution.
For example say x = 4 (x >1), (x^2 - 1) >= 0 hence, x>1 is not a solution.
x = 0.3, (x^2-1)<0, hence -1 <= x <= 1 is a solution.
Finally, x = -1.1, (x^2-1) > 0, hence x<-1 is not a solution.

The only choice that matches the above solution is E

This type of an inequality solution can be extended to x to the power 3, 4, 5 ....