Problem Solving

If b<2 and 2x-3b=0, which of the follwing must be true?

A. x>-3
B. x<2
C. x=3
D. x<3
D. x>3

pzazz12 wrote:If b<2 and 2x-3b=0, which of the follwing must be true?

A. x>-3
B. x<2
C. x=3
D. x<3
D. x>3

Hi there,

"Focus" on the question, that is, (from the alternative choices) you must find something about x... from the fact that 2x = 3b and that 3b < 3.2 = 6 , you know that 2x < 6, therefore x < 3.


Answer: D

Regards,
Fabio.

Hi,

Given information:
b<2
and 2x - 3b = 0, or 2x = 3b

As b<2 then 3b<6
Thus 2x<6 (as 2x = 3b), or
x<3

So D is the answer.

2x-3b = 0
b = 2x/3
since it is given that b<2 hence 2x/3 <2 or
2x <6 or
x<3

pzazz12 wrote:If b<2 and 2x-3b=0, which of the follwing must be true?

A. x>-3
B. x<2
C. x=3
D. x<3
D. x>3

The responses provided are both very helpful - I just want to add one more thing.

Whenever you're asked a question about a variable, and you're given a complex equation/inequality involving that variable, the first step you should almost always take is to isolate that variable.

From the question stem we don't know what the question is really asking - it's only by studying the choices (another thing you should do on EVERY problem solving question) that we realize that the question is really asking us to solve for x.

So, we isolate x in the original equation:

2x = 3b
x = (3/2)b

Since we know that b < 2, we can now solve:

x < (3/2)2

x < 3