Inequalities - When to combine and when not to

[pmmalkan+gmat]

If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 - 5x > -13

(2) 3 - 2x < -x + 4 < 7.2 - 2x

Normally, I would have solved this in the easiest and the most obvious way possible. That is:
1. Solve the If statement and get x > 2
2. Solve (1) and get x < 3.8 so I get x = integer 3 (SUFF.)
3. Solve (2) and also get the same result x = integer 3 (SUFF.)

However, I had seen Ron's Thursday lecture on combining inequalities just the day before and it kinda stuck in my head so I went ahead and combined the if statement inequality with stmt. (1) and I get a different result ->
I get x = integers 3 and 4.

Am I doing anything wrong conceptually? When should I combine and should I not?
I know in this problem it would be foolish to combine. But is it wrong as well? Any specific rule to combine?

Thanks very much,
Priya

[tim]

You haven't given any information about what you did to combine the statements, so it's possible you made an algebra mistake. In general, however, it's not wise to collapse two pieces of information into one piece if that's what you did, because you lose important information. If you can get useful information out of the two pieces of information separately, you should do so..

[yousuf_azim]

Dears.

What is the ANS?

BR

[JohnHarris]

However, I had seen Ron's Thursday lecture on combining inequalities ... get x = integers 3 and 4.

First, let's finish reducing the equations to get:
If x > 2, what is the value of the integer x?

(1) x < 3.8

(2) -1 < x < 3.2

combining either (1) or (2) with the given X> 2, we get
2 < x < 3 + d
where d is either 0.8 [for (1)] or 0.2 [for (2)]. So, as you indicated, the answer is 3 and both are sufficient individually.

If I'm understanding you correctly, you are referring to
a > b
c > d
implies
a + c > b + d
as is referred to in
guide3-inequalities-when-shud-we-really-add-two-inequalities-t9449.html
for example

To do the add properly we first have to have the inequalities pointing in the same direction so we have to re-write the if and (1) as
x > 2
3.8 > x
Adding now gives
x + 3.8 > x + 2
which just tells you 3.8 is greater than 2. If this not what you were referring to, you will have to give more details as mentioned by tim

[jnelson0612]

Dears.

What is the ANS?

BR

John, nice!

Yousuf, the answer is D.

[gmatwork]

If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 - 5x > -13

(2) 3 - 2x < -x + 4 < 7.2 - 2x


I did this question by combining the two inequalities -

Say combine 8x > 4 + 6x and stat 1 inequality I got x< 4.25 now just looking at this x can be any integer less than 4.25 and even if I combine x>2 (from question stem inequality I still get multiple values of x ...this leads me in wrong direction.

Instead if I do not combine two inequalities as suggested by OE, I do get only one integer solution. Now where does that leave me? I am not sure why combining two inequalities should provide a different solution than keeping them separate???

[tim]

there must be something you're doing wrong in combining the inequalities. can you tell us more about the steps you took?