Problem Solving

parveen110 wrote:Find the complete range of values of x for which |x+3|<2x-5.

a. (5/2, inf)
b. (-inf,5/2)
c. (8, inf)
d. (9, inf)
e. (2/3,inf)

I always get confused about the questions involving modulus. Please help.

Hi parveen110,

I appreciate that you feel that there is some merit in posting non-GMAT-style questions on Beat the GMAT, but you should know that posting these kinds of questions can cause great consternation for inexperienced students who don't know what the GMAT tests and what it doesn't test.

Your last post (https://www.beatthegmat.com/geometry-t277034.html#721072), which features the concept of "diagonals of a convex polygon [that] are concurrent," can easily FRUSTRATE students who aren't aware that the GMAT test-makers do not require us to understand the concept of "concurrent diagonals."

Likewise, the answer choices in the above question feature notation ("interval notation" to be precise) that students are NOT required to know. When students see this mysterious notation, many begin to doubt whether they are adequately prepared for the GMAT. This is a bad thing. Students preparing for the GMAT are already stressed out; they don't need to be exposed to questions that would never appear on the GMAT.

EXECUTIVE SUMMARY: While you may find that there is some merit to posting non-GMAT-style questions, the benefits of doing so DO NOT outweigh the potential harm of disrupting the preparation of other students. There are TONS AND TONS of great GMAT-style questions available from REPUTABLE GMAT prep companies (beginning with the companies that sponsor these forums). There's no need to post questions like that above.

Cheers,
Brent

parveen110 wrote:Find the complete range of values of x for which |x+3| < 2x-5.

a. (5/2, inf)
b. (-inf,5/2)
c. (8, inf)
d. (9, inf)
e. (2/3,inf)

Incidentally, this question COULD HAVE been written to be more GMAT-like.

Find the complete range of values of x for which |x+3| < 2x-5.
A) x > 5/2
B) x < 5/2
C) x > 8
D) x > 9
E) x > 2/3

An easy approach here is to test some values.
Let's see if x = 3 is a solution to the given inequality.
Plug in x = 3 to get: |3+3| < 2(3)-5
Evaluate to get: 6 < 1
NOPE.
x = 3 is NOT a solution to the given inequality. So, any answer choice that includes 3 as a possible value of x is incorrect.
So, we can ELIMINATE A and E.

Now let's see if x = 8.5 is a solution to the given inequality.
Plug in x = 8.5 to get: |8.5+3| < 2(8.5)-5
Evaluate to get: 11.5 < 12
GOOD
x = 8.5 IS a solution to the given inequality. So, any answer choice that DOES NOT include 8.5 as a possible value of x is incorrect.
We can now ELIMINATE B and D

By the process of eliminate, the answer is C

Cheers,
Brent