The number n satisfies the relationship n > 0. Write three inequalities to express the relationship between n and 1/n.
THANK YOU!
If n<1, n < 1/n
If n=1, n = 1/n
If n>1, n > 1/n
Write an inequality to express the relationship of -12.3 and -12.03 *
Equals -12.3 > -12.03
To express the relationship between n and 1/n, we can write three inequalities as follows:
1) n > 0 : This is the given relationship that n is greater than 0.
2) n * (1/n) > 0 : This inequality states that the product of n and 1/n is greater than 0, implying that both n and 1/n must be either positive or negative.
3) n^2 / n > 0 : This inequality involves squaring n and dividing by n. Since n > 0, dividing by a positive value preserves the inequality, resulting in n > 0.
To express the relationship between n and 1/n, we need to follow these steps:
Step 1: Start with the given relationship "n > 0".
Step 2: Express 1/n. To do this, we can take the reciprocal of both sides of the inequality. Since n > 0, we know n is positive, so we can safely take the reciprocal without changing the direction of the inequality.
Reciprocal of 1/n is n/1, which simplifies to just n.
So, 1/n is simply n.
Step 3: Write the three inequalities:
1) n > 0 (the original relationship)
2) n > 1/n (which is essentially n > n)
3) 1/n > 0 (which is essentially n > 0)
These three inequalities express the relationship between n and 1/n.