Question

The set of all real numbers satisfying the inequality \( x - 2 < 1 \) is:

• A. \( (3, \infty) \)
• B. \( [3, \infty) \)
• C. \( [-3, \infty) \)
• D. \( (-\infty, -3) \)
• E. \( (-\infty, 3) \)

Hint:

Use parentheses \( ( \ ) \) for strict inequalities (\(\)) and brackets \( [ \ ] \) for inclusive ones (\(\leq,\geq\)).

Answer 1

Answer: (E)

Concept: To solve a linear inequality, isolate the variable just like an equation. The solution represents a range of values, which is written in interval notation.

Step 1: Isolate the variable \( x \).
Given: \[ x - 2 < 1 \] Add 2 to both sides: \[ x < 1 + 2 \] \[ x < 3 \]

Step 2: Write the solution in interval form.
All values less than 3 are included, but 3 is not included. \[ (-\infty, 3) \]

Step 3: Final answer.
\[ \boxed{(-\infty, 3)} \]