Question

what happens to the value of the expression \\(\frac{5}{x} + 5\\) as \\(x\\) decreases from a large positive number to a small positive number?

choose 1 answer:

a it increases.

b it decreases.

c it stays the same.

Explanation:

Step1: Analyze the term $\frac{5}{x}$

For positive \( x \), as \( x \) decreases (from large to small positive number), the value of \( \frac{5}{x} \) increases. For example, if \( x = 10 \), \( \frac{5}{10}=0.5 \); if \( x = 5 \), \( \frac{5}{5} = 1 \); if \( x = 1 \), \( \frac{5}{1}=5 \). As \( x \) gets smaller, \( \frac{5}{x} \) gets larger.

Step2: Analyze the whole expression $\frac{5}{x}+5$

The expression is \( \frac{5}{x}+5 \). The second term \( 5 \) is a constant. Since \( \frac{5}{x} \) increases as \( x \) decreases (for positive \( x \)), adding a constant (\( 5 \)) to an increasing term will result in the whole expression increasing. So as \( x \) decreases from a large positive number to a small positive number, \( \frac{5}{x}+5 \) increases.

Answer:

A. It increases.