sanaa.rizwan wrote:if b<2 and 2x - 3b = 0, which of the following must be true

a. x >-3
b. x < 2
c. x =3
d. x < 3
e. x > 3

An alternate approach is to show that four of the five answer choices DON'T have to be true.

Answer choice A: x > -3.
Test a value LESS than -3.
If we substitute x=-4 into 2x=3b, we get:
2(-4) = 3b
-8/3 = b.
Since b=-8/3 satisfies the constraint that b<2, it's possible that x=-4.
Eliminate A, C, and E, none of which includes x=-4 within its range.

Answer choice B: x < 2
Answer choice D: x < 3
Test a value BETWEEN 2 and 3.
If we substitute x=2.5 into 2x=3b, we get:
2(2.5) = 3b
b = 5/3.
Since b=5/3 satisfies the constraint that b<2, it's possible that x=2.5.
Eliminate B, which does not include x=2.5 within its range.

The correct answer is D.

if b<2 and 2x - 3b = 0, which of the following must be true

a. x >-3
b. x < 2
c. x =3
d. x < 3
e. x > 3

here is how I am solving this question

if b<2 then b = {1,0,-1,-2...}

solving for x

2x - 3b = 0
2x = 3b
x = 3/2b or 1.5 b

since the highest possible value of b = 1, then highest possible value of x = 1.5 hence x<2 which is B

Correct answer is D

Can you explain how, Am I suppose to take b = {1.9, 1.8,1.7....} to solve these type questions or only integer values

Hi Sanna,
I wouldn't try to plug values and check for the answers in my first attempt for such questions.
This can be easily solved as the experts have solved it without plugging in answers.