For what values of y does the binomial 5y-7 belong to the interval (-5, 13) ?

Answer: y should be in the interval (0.4, 4)

Explanation:

The binomial 5y - 7 is in the interval (-5, 13) if and only if

-5 < 5y - 7 < 13

Solving the inequalities in this form is the same as solving equation. So, we add all sides of the inequalities by 7 so that

2 < 5y < 20

Then, we divide both sides by 5 to get the following inequalities

0.4 < y < 4

Hence y should be in the open interval (0.4, 4).