Question

two positive integers are 3 units apart on a number line. their product is 108. which equation can be used to solve for m, the greater integer? \\(\bigcirc\\) \\(m(m - 3) = 108\\) \\(\bigcirc\\) \\(m(m + 3) = 108\\) \\(\bigcirc\\) \\((m + 3)(m - 3) = 108\\) \\(\bigcirc\\) \\((m - 12)(m - 9) = 108\\)

Explanation:

Step1: Define the smaller integer

Since the two positive integers are 3 units apart and \( m \) is the greater integer, the smaller integer will be \( m - 3 \) (because the greater number minus 3 gives the smaller one when they are 3 units apart).

Step2: Set up the product equation

The product of the two integers is 108. The two integers are \( m \) (greater) and \( m - 3 \) (smaller). So, the product of these two integers is \( m\times(m - 3) \), and this product is equal to 108. So the equation is \( m(m - 3)=108 \).

Answer:

\( m(m - 3)=108 \) (the first option)