Greatest Possible Integer Solution

Question

What is the Greatest Possible Integer Solution of the Inequality 3.829x < 28.195

Answer 1

3.829x < 28.195

x < 28.195/3.829

x < 7.364

Therefore, the largest INTEGER value x can take is:

x = 7

Answer 2

An integer is defined as a whole number, essentially a number that is not a fraction. For example, integers include: -5, 1, 17, 322 whereas non-integers include: -4.33, 2/3, 3.14, 55.1

To find the greatest possible integer solution of 3.829x < 28.195 lets first imagine it as if it was not an inequality.

Lets solve 3.829x = 28.195

x = 28.195/3.829

x = 7.3635

7.3635 is not an integer but lets plug the two surrounding integers back into the original problem and see which works. The two closest integers to 7.3635 are 7 (below) and 8 (above).

Lets try x = 8

3.829(x) < 28.195?

3.829(8) < 28.195?

30.632 <28.195?

FALSE... x cannot equal 8 since 30.632 is not less than 28.195

Lets try x = 7

3.829(x) < 28.195?

3.829(7) < 28.195?

26.803 <28.195?

TRUE... x can equal 7 sine 26.803 is less than 28.195

Therefore, the greatest possible integer solution is x = 7

I hope this is helpful!