Solve the linear inequality 3b - 7 < 32. Choose the correct description of the solution set for the real number b.

Introduction:
This question tests solving a one-variable linear inequality. Unlike an equation, an inequality describes a range of values. The main rules are: you can add or subtract the same number from both sides without changing the inequality sign, and you can divide by a positive number without flipping the sign. Here we isolate b by first adding 7 and then dividing by 3.

Given Data / Assumptions:

• Inequality: 3b - 7 < 32
• b is a real number
• Operations used: addition/subtraction and division by a positive number

Concept / Approach:
Rearrange the inequality step-by-step to isolate b. Since 3 is positive, dividing by 3 will not reverse the inequality sign. The final result should be expressed as a comparison like b < some number, representing all valid solutions.

Step-by-Step Solution:
Start: 3b - 7 < 32 Add 7 to both sides: 3b < 39 Divide both sides by 3: b < 13

Verification / Alternative check:
Test a value less than 13, say b = 12: 3*12 - 7 = 36 - 7 = 29, and 29 < 32 is true. Test b = 13: 3*13 - 7 = 39 - 7 = 32, and 32 < 32 is false. So b must be strictly less than 13.

Why Other Options Are Wrong:
b ≤ 13 incorrectly includes 13 which fails the strict “<”. b ≥ 13 and b > 13 give values that make the left side 32 or more. b = 13 is not valid because equality is not allowed here.

Common Pitfalls:
Confusing < with ≤, or mistakenly reversing the inequality sign (which would happen only if dividing by a negative number, not in this problem).

Final Answer:
The solution set is b < 13.