write a compound inequality that represents the situation. all real numbers at least –6 and at most 3 a. –6 < x ≤ 3 b. –6 < x < 3 c. –6 ≤ x ≤ 3 d. –6 ≥ x ≥ 3
All real numbers at least –6 and at most 3 is given by: \(-6 \leq x \leq 3\)
Answer: c. –6 ≤ x ≤ 3
Step-by-step explanation:
Given situation: All real numbers at least –6 and at most 3.
Let x be a real number
and "at least" means the minimum value , so 'x' must b greater than or equal to the minimum value i.e. –6 ≤ x .
"at most" means the maximum value , so 'x' must be smaller than or equal to the maximum value i.e. x ≤ 3 .
then according to the given situation,
All real numbers at least –6 and at most 3.
⇒ –6 ≤ x ≤ 3