Question

Two different points on a number line are both 3 units from the point with coordinate -4 . The solution to which of the following equations gives the coordinates of both points?

Answer 1

To locate two points that are 3 units away from -4 on a number line, we find the points -1 and -7 using the equation |x + 4| = 3, which covers both directions from the central point.

Step-by-step explanation:

To find the coordinates of two points on a number line that are 3 units away from the point with coordinate -4, we consider one point to be -4 + 3 and the other to be -4 - 3. This leads us to calculate the coordinates as follows:

The point to the left of -4 is -4 - 3 = -7.

The equation that gives the coordinates of both points is |x + 4| = 3, because the absolute value represents the distance from -4 on the number line, and it can be either to the right or left of -4, hence the two solutions -1 and -7.