Question

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

Answer 1

Answer: c. –6 ≤ x ≤ 3

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

Answer 2

All real numbers at least –6 and at most 3 is given by:
`-6 \leq x \leq 3`