for what integer value of m is 2m +14 > 42 and 5 < m/4 + 3 < 7?

Answer 1

I would recommend breaking this up into 3 separate inequalities and solve each of them individually, then compare.

2m + 14 > 42

2m > 28

m > 14

5 < m/4 + 3

2 < m/4

8 < m

m/4 + 3 < 7

m/4 < 4

m < 16

The 2nd inequality doesn't give us any new information that we didn't already know from the 1st. But the 1st and 3rd inequalities tell us that m > 14 (m is more than 14) and m < 16 (m is less than 16). If m has to be an integer between 14 and 16, it must be 15. So,

m = 15