# Determine the set of natural numbers n if 2/5=<(n+1)/10=<1/2

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### 3 Answers

We have to determine the set of natural numbers in which n lies given that : 2/5=<(n+1)/10=<1/2

2/5=<(n+1)/10=<1/2

multiply all the terms by 10

=> 4 =< (n +1) =< 5

subtract 1 from all the terms

=> 4 - 1 =< n + 1 - 1 =< 5 - 1

=> 3 =< n =< 4

**Therefore n lies in the set [ 3 , 4]**

To find the solutions for n in natural numbers:

2/5 =< (n+1)/10 =< 1/2.

We multiply by 10 throughout.

2*10/5 =< n+1 =< 1/2*10 = 5.

4 = < n+1 = < 5.

We subtract 1 f:

4-1 = < n =< 5-1.

3 = < n = < 4..

Therefore the solution for n is the natural numbers 3 and 4.

We'll multiply the inequality by 10:

10*2/5 =< 10*(n+1)/10 = < 10/2

We'll simplify and we'll get:

4 =< n + 1 =< 5

We'll solve the left inequality:

4 =< n + 1

We'll subtract 1:

n >= 3

We'll solve the right inequality:

n + 1 =< 5

We'll subtract 1:

n =< 4

**The n natural values of the set are: {3 ; 4}.**