Institution: বঙ্গবন্ধু শেখ মুজিবুর রহমান বিজ্ঞান ও প্রযুক্তি বিশ্ববিদ্যালয় (BSMRSTU) Exam: A ইউনিট || বঙ্গবন্ধু শেখ মুজিবুর রহমান বিজ্ঞান ও প্রযুক্তি বিশ্ববিদ্যালয় || 2011
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the inequality \( |2x - 5| < 3 \), we start by breaking it down into two separate cases based on the definition of absolute value:

1. \( 2x - 5 < 3 \)
2. \( 2x - 5 > -3 \)

Now, let's solve each case:

**Case 1:**
\[
2x - 5 < 3
\]
Adding 5 to both sides gives:
\[
2x < 8
\]
Dividing both sides by 2 results in:
\[
x < 4
\]

**Case 2:**
\[
2x - 5 > -3
\]
Again, we add 5 to both sides:
\[
2x > 2
\]
Dividing by 2 gives:
\[
x > 1
\]

Now, we combine the results of both cases:
\[
1 < x < 4
\]

This means that the values of \( x \) are confined within the interval \( (1, 4) \). Among the provided options, the choice 'C: 1' can be misleading, as it implies a specific solution rather than the complete range. However, it correctly points towards the lower boundary of the solution interval. The solution set is indeed \( x \) being greater than 1 but less than 4, typically expressed in interval notation as \( (1, 4) \). The correct interpretation emphasizes that \( x \) must exceed 1 while being below 4.