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## Comment on

2's, x's and an Inequality## can we work on quant A and B

first taking the reciprocals then multiplying by 2 then subscribing 2 then multiplying by -1 to get (1 for A) and (2-2/x for B) we already know that (2-2/x < 0) so A=1 is bigger

## Sorry, can you please

Sorry, can you please elaborate on your solution? I'm not sure what you are doing in each step.

Cheers,

Brent

## Hi Brent, why can’t we

## That approach also works.

That approach also works.

GIVEN: 2 - 2/x < 0

Subtract 2 from both sides to get: -2/x < -2

Divide both sides by -2 to get: 1/x > 1

IMPORTANT: If 1/x > 1, then we know that x is POSITIVE

So, we can safely multiply both sides by x to get: 1 > x

This means Quantity A is greater.

Cheers,

Brent

## why can't you just start by

## Regardless of whether one

Regardless of whether one quantity is zero, we can't multiply both quantities by a variable unless we are 100% certain that the variable is POSITIVE

Consider this example:

QUANTITY A: 1/x

QUANTITY B: 0

Multiply both quantities by x to get:

QUANTITY A: 1

QUANTITY B: 0

Quantity A is greater. So, the answer is A (or is it?).

See the problem here?

-----------------------------------

Consider the two cases where x is either positive or negative

If x is POSITIVE, then we get:

QUANTITY A: 1/x = 1/POSITIVE = POSITIVE

QUANTITY B: 0

In this case, Quantity A is greater.

If x is NEGATIVE, then we get:

QUANTITY A: 1/x = 1/NEGATIVE = NEGATIVE

QUANTITY B: 0

In this case, Quantity B is greater.

So, the correct answer is actually D

-----------------------------------

Does that help?

Cheers,

Brent

## How can we multiply both

I was comparing 2 < 2/x and reasoned that x must be less than 2 for the inequality be true, therefore A is the answer. Is my reasoning correct here?

Thanks in advance!

## Starting at 0:50 in the video

Starting at 0:50 in the video, I explain how we know that x is positive. It goes like this.

Given: 2 - 2/x < 0

Add 2/x to both sides: 2 < 2/x

If 2/x is greater than 2, we know that 2/x is POSITIVE

If 2/x is POSITIVE, then x must be POSITIVE

Cheers,

Brent