For which values of x is |x + 3| ≥ 5?
Correct answer: A. x ≤ −8 or x ≥ 2
- A. x ≤ −8 or x ≥ 2
- B. −8 ≤ x ≤ 2
- C. x < −8 or x > 2
- D. −2 ≤ x ≤ 8
Explanation
An absolute value of at least 5 means x + 3 ≤ −5 or x + 3 ≥ 5. These conditions give x ≤ −8 or x ≥ 2, including both endpoints.
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Linear equations are solved using algebraic manipulation, while quadratic equations involve factorisation, the quadratic formula, completing the square and the discriminant. Inequalities require careful treatment of solution intervals and reversal of the sign when multiplying or dividing by a negative number, unlike ordinary equation solving.
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