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apkaann
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General Rule: Inequalities 25 Jul 2022, 08:02
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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
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General Rule: Inequalities 25 Jul 2022, 08:14
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check below question and Bunuel explaination this should be of help:

https://gmatclub.com/forum/if-r-s-2t-is ... l#p1064950
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General Rule: Inequalities 25 Jul 2022, 08:38
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apkaann
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
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
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General Rule: Inequalities 25 Jul 2022, 09:51
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apkaann
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

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!
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General Rule: Inequalities 27 Jul 2022, 16:10
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apkaann
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

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.
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General Rule: Inequalities 28 Jul 2022, 21:56
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apkaann
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

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.

Thank you Scott, this helps.
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General Rule: Inequalities 28 Jul 2022, 21:57
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Thank you for directing me to the resources.

-A
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General Rule: Inequalities 01 Aug 2022, 17:58
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apkaann
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

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.

Thank you Scott, this helps.

Of course.
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General Rule: Inequalities 02 Aug 2022, 10:52
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apkaann
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apkaann
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

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.

Thank you Scott, this helps.

Of course.
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