Plugging in answer choices as suggested above is a great way to solve if you aren't super comfortable with absolute value equations, but you can also solve by manipulating the equation.

|5b-7| < 1
-1 < 5b - 7 < 1
6 < 5b < 8
6/5<b<8/5

B is the only answer choice that is between 6/5 and 8/5, so it's the correct answer.

ardz24 wrote:Which of the following could be b if |5b - 7| < 1?

A. -7/5
B. 3/2
C. 8/5
D. 2
E. 0

We will consider 2 separate cases: when (5b - 7) is positive and when (5b - 7) is negative.

Case 1: (5b - 7) is positive:

5b - 7 < 1

5b < 8

b < 8/5

Case 2: (5b - 7) is negative:

-(5b - 7) < 1

-5b + 7 < 1

-5b < -6

b > 6/5

Thus, 6/5 < b < 8/5, or 1.2 < b < 1.6. Since 3/2 = 1.5, b could be 3/2.

Answer: B

BTGmoderatorAT wrote:Which of the following could be b if |5b - 7| < 1?

A. -7/5
B. 3/2
C. 8/5
D. 2
E. 0

Is there a strategic approach to this question? Can any experts help?

When we have an absolute value "less than" inequality, we create a "between" statement to solve it. Thus, we have:

-1 < 5b - 7 < 1

6 < 5b < 8

6/5 < b < 8/5

We are looking in the answer choices for a value between 6/5 and 8/5. We see that when b is 3/2, |5b - 7| < 1.

Answer: B