Is the answer to this question really A as given in the solution. When choosing numbers, x and z can be negative or positive, as no restrictions are given. If x is -ve and z is +ve, won’t x - z be < 0. And if x,z is +ve won’t x-z> 0. hence answer shuld be D right? Or am I missing something?
-y < -z and adding this with the first inequality gets you to x - z > y - y = 0
What numbers did you choose?
x > y > z so x > z. Thus, your assertion contradicts the constraints established in the question.
To reiterate, since x > z then subtracting z from both sides would still get you to x - z > 0.
Thanks for the clarification. I completely missed that x should be greater than z, when I chose negative nos for x and positive for z.
The answer given in the solution is D now. Shouldn’t it be Option B.
In this problem, we are given:
x > y
x > z
The question asks us to compare y - z to 0.
In the video, it’s mentioned that inequalities can sometimes be added or subtracted. So I tried manipulating the second inequality as follows:
Multiply the second inequality (x > z) by -1, which gives: -x < -z
Then I added this to the first inequality (x > y), resulting in:
x + (-x) > y + (-z), which simplifies to:
0 > y - z, or y - z < 0
Based on this, I concluded that Quantity A is less than Quantity B.
My doubt is: Is this method always valid? Can we reliably manipulate inequalities this way—especially by multiplying one of them by -1 and adding it to the other—to compare expressions like y - z? Or does this only work under specific conditions?
Would really appreciate any clarification you could provide!
It’s unclear how you propose to add two inequalities with differing inequality signs (−x < −z and x > y).
You can instead construct counterexamples for this case:
Case 1: (x,y,z) = (3,2,-1) so y - z > 0
Case 2: (x,y,z) = (3,-1,2) so y - z < 0