Solving 2x + 3 ≤ 11, we subtract 3 from both sides to get 2x ≤ 8. Dividing both sides by 2 yields x ≤ 4. On the real number line, this corresponds to all numbers less than or equal to 4. In interval notation, that set is written as (−∞, 4], with a square bracket at 4 indicating that 4 is included.
Option A:
Option A, (−∞, 4), excludes 4 itself and would represent x < 4, which is a strict inequality, not the given ≤ relation.
Option B:
Option B correctly captures x ≤ 4 by including all values up to and including 4, thus satisfying the inequality exactly.
Option C:
Option C, (−∞, 7], includes many values greater than 4, violating the upper bound imposed by 2x ≤ 8.
Option D:
Option D, [4, ∞), represents x ≥ 4, the opposite direction of the inequality, and only includes 4 and greater values.
Comment Your Answer
Please login to comment your answer.
Sign In
Sign Up