Addition and subtraction in inequality in any case is accepted:
(A) 6c-3 ? (B)3c-5 just solve it like algebraic expressions.
3C ? -2 Simple addition and subtraction on both sides.
C ? -2/3 Dividing by 3(being positive no.) on both sides is accepted.
Since c<–1, (B) is the answer.

We can solve this question using matching operations

Given:
Quantity A: \(6c-3\)
Quantity B: \(3c-5\)

Add \(3\) to both quantities to get:
Quantity A: \(6c\)
Quantity B: \(3c-2\)

Subtract \(3c\) from both quantities to get:
Quantity A: \(3c\)
Quantity B: \(-2\)

Divide both quantities by \(3\) to get:
Quantity A: \(c\)
Quantity B: \(-\frac{2}{3}\)

Since \(-1 < -\frac{2}{3}\), and since it's given that \(c < –1\), we can combine both inequalities to get: \(c < -1 < -\frac{2}{3}\)
This means \(c < -\frac{2}{3}\), so Quantity B is greater.

Answer: B


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Even if \(C = -1 \)(extreme value)

Quantity A is \(6(-1) - 3\) compared to Quantity B \(3(-1) - 5\)

\(-6 - 3\) compared to \(-3 - 5\)

\(- 9 \) < \(-8\)

When \(C < -1\), we can expect this inequality to hold even more so.

Therefore, answer is Quantity B.

can someone explain why my method was wrong?

I did
6c-3 3c-5

Multiply QB by 2 so it's comparable to QA --> 6c-3 6c-10

get rid of 6c on both sides ---> -3 -10

-3 > -10 --> QA

I don't understand why my way of simplifying resulted in the wrong answer

This question is way more simple than it looks like especially if you work conceptually on the number line

Suppose c is -2

A is -12-3=-15

B is -6-5=-1 B >A

going further on the negative side of the number line LHS A becomes even more negative than B which will be always close to zero than A

So the answer is B

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