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

10 < 6n -2 ≤ 34

n= {3, 4, 5, 6}

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}

Answer 2

[2,6]

Explanation:

Translate to an inequality. Since two less than six times her number is at least ten and at most thirty-four, we have the following inequality.

10≤6n−2≤34

Solve the compound inequality by isolating the variable in the center.

10≤6n−2≤3412≤6n≤362≤n≤6

Finally, write your answer in interval notation. The inequality includes all values between 2 and 6 including the end values, therefore the final answer is:

[2,6].