Question

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

Write your answer in interval notation. For example −3

Answer 1

Answer:6≥n≥2

Explanation:

34 ≥ 6n-2≥10

If 6n-2 is ¨no more than 34¨ it means it is less than or equal to 34 and if it is ¨at least 10" 6n-2 is 10 or more than it.

So now let´s separate these into two separate equations:

1.34≥6n-2

+2 +2

30≥6n

30/6≥6/6n

6≥n

2.6n-2≥10

+2 +2

6n≥12

6/6n≥12/6

n≥2

Now let's see what our compound inequality means...

n is greater or equal to two but is less than or equal to six

so our compound is

6≥n≥2

Hope this helps!!