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:

Let the greater integer be \( m \). Since the two positive integers are 3 units apart on the number line, the smaller integer will be \( m - 3 \) (because the greater one is \( m \), so subtracting 3 gives the smaller one). The product of the two integers is 108, so the equation is \( m(m - 3)=108 \). We can check the other options: \( m(m + 3) = 108 \) would imply the smaller integer is \( m+3 \), which is larger than \( m \), so that's incorrect. \( (m + 3)(m - 3)=108 \) is a difference of squares and doesn't represent the product of two numbers 3 units apart in the way we need. \( (m - 12)(m - 9)=108 \) assumes specific values (12 and 9) but we don't know that yet; we just know the difference is 3, so this is not the general equation to solve for \( m \).

Answer:

A. \( m(m - 3) = 108 \)