Absolute value inequality: split, then count integers

Correct answer: B

Rewrite the absolute value as a compound inequality:

−5 < 2x − 3 < 5

Add 3 to all three parts: −2 < 2x < 8.

Divide by 2: −1 < x < 4.

The integers strictly between −1 and 4 are 0, 1, 2, 3. That is 4 integers.

The two edge mistakes to avoid:

• Strict inequalities exclude the endpoints. x = −1 and x = 4 do not qualify. Including them gives 6, trap (D). If the symbol were ≤, both endpoints would count.
• (E) looks tempting if you confuse |2x − 3| < 5 with |2x − 3| > 5. A “less than” absolute value traps x in a bounded window, so the solution set is finite. A “greater than” version would give two unbounded rays and infinitely many integers.

Quick verification at the boundary: x = 0 gives |−3| = 3 < 5 ✓; x = 4 gives |5| = 5, which fails the strict inequality, correctly excluded.