# natural numberit is a natural number x for (3+x)/5<1 to be true?

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### 3 Answers

You should solve the inequality such that:

(3+x)/5<1 => 3+x<5

=> x<5-3 => x<2

Notice that the problem requires only the natural numbers that satisfy the inequality, hence, here are the values of x: x in {0,1}.

(3+x)/5 < 1

We need to find x such that x is a natural number.

==> We will solve the inequality.

==> We will multiply by 5.

==> 3+ x < 5

Now we will subtract 3 from both sides.

==> x < 5-3

==> x < 2

**Since x is a natural number, then x = { 0,1}**

We'll subtract 1 both sides:

(3+x)/5 - 1<1 - 1

We'll get:

(3+x)/5 - 1< 0

We'll multiply by 5:

(3 + x - 5)/5 < 0

(x - 2)/5 < 0

If the ratio is negative, then the numerator and denominator have opposite signs. Since the denominator is positive, only the numerator could be negative.

x - 2 < 0

We'll add 2:

x < 2

**The natural numbers that makes the ratio (3+x)/5<1 are x = 0 and x = 1.**