Question

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

Answer 1

The correct answer is:

from y=2/5 to y=4.

Explanation:

To solve this, we set the binomial equal to each end of the interval and solve for y.

First the lower end:
-5=5y-7

Add 7 to both sides:
-5+7=5y-7+7
2=5y.

Divide both sides by 5:
2/5 = 5y/5
2/5 = y.

This gives us the lowest value of y that puts the binomial in this interval.

Now we follow the same process for the upper end of the interval:
13=5y-7

Add 7 to both sides:
13+7=5y-7+7
20=5y.

Divide both sides by 5:
20/5=5y/5
4=y.

This means that the highest value of y that will put the binomial in this interval is 4.

Answer 2

Answer:
[0.4,4]

Step-by-step explanation:
The get the values of y belonging to the given interval, we will simply solve the following inequality:
-5 ≤ 5y - 7 ≤ 13
-5 + 7 ≤ 5y ≤ 13 + 7
2 ≤ 5y ≤ 20
2/5 ≤ y ≤ 20/5
0.4 ≤ y ≤ 4

Hope this helps :)