Is a + 2b < c + 2d?

[GMAT143]

MGMT says that two inequalities can be added if the signs are facing the same direction, and two inequalities can be multiplied if all expressions are positive.

Why should we not subtract or divide two inequalities? I read online that two inequalities can be subtracted if the signs are facing opposite directions, and two inequalities can be divided if all expressions are positive and the signs are facing opposite directions.

For evaluation statement 1 below, why can't we say that since a<c, 2b<2d?

MGMT book for Equations, Inequalities and VICS (Ed. 4, pg. 88):

MGMT question:

Is a + 2b < c + 2d?

(1) a < c
(2) d > b

MGMT answer:

For this problem, we can add the inequalities together to make them match the question.
First, we need to line up the inequalities so that they are all facing the same direction:
a < c
b < d

Then we can take the sum of the two inequalities to prove the result. We will need to add
the second inequality TWICE:
a < c
+ b< d
a+ b < c+ d
+ b< d
a+2b < c+ 2d
If you use both statements, you can answer the question. Therefore the answer is (C).

[RonPurewal]

sorry, but i can't tell what you are asking here.

you're clearly asking whether some particular step of algebra can be performed.
so—could you write out the actual work / steps that you're wondering about?
i.e., something like "Can you do this:", followed by the actual steps.

thanks.