Word problem, linear equation

Question

Gregory is thinking of a number and he wants his sister Lauren to guess the number. His first clue is that six less than twice his number is between four and forty-two. Write a compound inequality that shows the range of numbers that Gregory might be thinking of.

Answer 1

Let X = the number

2X-6 is between 4 and 42

4 < 2X-6 < 42

Add 6

4+6 < 2X < 42 + 6

10 < 2X < 48

divide by 2

5 < X < 48/5

Make those inequalities into less than or equal to signs so X could be anywhere in the interval [5,48/5] or [5,9.6]

the number is somewhere between 5 and 9.6