Question

Alice is thinking of a number n that she wants her sister to guess. Her first clue is that two less than six times her number is between ten and thirty-four (inclusive). Write a compound inequality that shows the range of numbers that Alice might be thinking of.

Answer 1

Answer:

10 < 6n -2 ≤ 34

n= {3, 4, 5, 6}

Step-by-step explanation:

number

⇒ n

two less than six times the number

⇒ 6n -2

it is between ten and thirty-four (inclusive)

⇒ 10 < 6n -2 ≤ 34

we can solve it as:

• 10 < 6n -2 ≤ 34     ⇒ add 2 to all sides
• 12 < 6n ≤ 36          ⇒ divide by 6 all sides
• 2 < n  ≤ 6
• n= (2, 6]

or

• n= {3, 4, 5, 6}