Question

write an inequality for the situation. all real numbers at most –9.5 or at least 5.5 a. –9.5 ≤ b ≤ 5.5 b. b ≤ –9.5 or b ≤ 5.5 c. b ≤ –9.5 or b ≥ 5.5 d. b ≥ –9.5 or b ≥ 5.5

Answer 1

Answer: b ≤ -9.5 or b ≥ 5.5

Explanation:

We use different sign for different statement that showing inequality,

Less than = <

More than = >

Less than equal to = ≤

More than equal to = ≥

Let b shows the real number,

The value of b is at least 5.5,

⇒ All real numbers more than 5.5 including 5.5,

⇒ b ≥ 5.5,

or If the value of b is at most -9.5,

⇒ All real numbers less than -9.5 including -9.5,

⇒ b ≤ -9.5

Thus, the required inequality is b ≤ -9.5 or b ≥ 5.5

Answer 2

All real numbers at most –9.5 or at least 5.5 is given by
`b \leq -9.5` or
`b \geq 5.5`