General Rule: Inequalities

Question

Experts,

Could you please guide if there is a general rule to mathematical operations that could be performed on a two sides of an inequality, like the ones below: 
1. Adding a constant
2. Multiplying/dividing with/by a positive number.

Especially relating to exponents, for example taking sq. root or cubing?

Thank you,
-A

Archit3110 · Answer

check below question and Bunuel explaination this should be of help: https://gmatclub.com/forum/if-r-s-2t-is ... l#p1064950

AndrewN · Answer

Hello,  apkaann . I would recommend checking out Section 9, "Inequalities," from the  Ultimate GMAT Quantitative Megathread . It should help you with any related queries you would have.

Good luck with your studies.

- Andrew

GMATWhizTeam · Answer

Hi apkaann

You may find these helpful:

Number-line Method|Easy Method to solve Inequalities & Exponents Algebra questions

Number Line and Inference: The Key to Solve Any Inequalities Problem

This should help!

ScottTargetTestPrep · Answer

You can take square roots of each side of an inequality as long as both sides are nonnegative.

As for exponents, it depends whether the exponent is even or odd. If the exponent is even, then you can only raise each side to that exponent of both sides are nonnegative. However, with odd exponents, there is no such restriction. You can always raise each side of an inequality to an odd exponent. In particular, you can always take the cube of each side of an inequality.

apkaann · Answer

Thank you Scott, this helps.

apkaann · Answer

Thank you for directing me to the resources.

-A

ScottTargetTestPrep · Answer

Of course.

ScottTargetTestPrep · Answer

Of course.

General Rule: Inequalities

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards