Question

suppose that e and f are points on the number line. if ef=13 and e lies at 3, where could f be located? if there are several locations, separate them with commas.

Explanation:

Step1: Recall the distance formula on a number line

The distance between two points \( E \) and \( F \) on a number line is given by \( |F - E| = EF \). We know \( E = 3 \) and \( EF = 13 \), so we have the equation \( |F - 3| = 13 \).

Step2: Solve the absolute value equation

Case 1: \( F - 3 = 13 \)
Solving for \( F \), we add 3 to both sides: \( F = 13 + 3 = 16 \).

Case 2: \( F - 3 = - 13 \)
Solving for \( F \), we add 3 to both sides: \( F = - 13 + 3 = - 10 \).

Answer:

-10, 16