Question

what is the sum of all integers $n$ that satisfy $-3n < 7n-20 < 3n~?$ in other words, what is the sum of all integers $n$ that satisfy both of the inequalities $-3n<7n-20\text{~~and~~}7n-20<3n~?$

Answer 1

3+4=7 is the total of all possible integer values of n.

What are integers?

Integers include zero, a positive natural number, and a negative integer represented by a minus sign.

The negative numbers are the inverse additions of the comparable positive numbers.

In mathematical notation, the letter Z is widely used to denote a set of numbers.

An integer is a whole number that can be positive, negative, or zero and is not a fraction.

Integer examples include -5, 1, 5, 8, 97, and 3,043.

So, the two inequalities are resolved independently. We add 3n to both sides of the first inequality, -3n7n-20, to find the solution:

Then, we add 20 to both sides to get 010n-20:

20<10n.

Lastly, multiplying both sides by 10 yields 2n, indicating that n must be bigger than 2.

We deduct 3n from both sides of the second inequality, 7n-203n:

Add 20 on both sides of 4n-200 to obtain:

4n<20.

Lastly, n must be less than 5 since the result of dividing both sides by 4 is n5.

Only the numbers 3 and 4 are greater than 2 and less than 5.

Therefore, 3+4=7 is the total of all possible integer values of n.

Know more about integers here:

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