Solving Inequalities: Need Help with Part (a)?

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To solve the inequality in part (a), start by expressing the difference between the two quantities involved. This foundational step will help clarify the relationship and guide further calculations. It is essential to isolate the variable to find the solution set. Seeking hints or guidance can be beneficial for understanding the process. Engaging with others can enhance problem-solving skills in inequalities.
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Homework Statement
An object, constrained to move along the x axis, travels a dis-
tance d1 with constant velocity v1 for a time t1 . It then instan-
taneously changes its velocity to a constant v2 for a time t2 ,
traveling a distance d2 . (a) Show that (v1d1+v2d2)/(d1+d2) is greater than or equal to (v1t1+v2t2)/(t1+t2).
(b) Under what conditions is this an equality?
Relevant Equations
v = v0 + at
x = x0 + v0t + (at^2/2)
I’m not sure of how begin solving for the inequality. How do I begin solving part (a)? Could I have a hint? Thank you!
 
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A good start would be to write the expression for the difference between them.
 
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Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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