Ontario Mathematics Proficiency Practice Test

To solve the equation |x - 3| = 7, we start by recalling the definition of absolute value. The equation |x - 3| = 7 means that the expression inside the absolute value can equal either 7 or -7.

This gives rise to two separate equations:

1. x - 3 = 7

2. x - 3 = -7

Starting with the first equation, we can add 3 to both sides to isolate x:

x - 3 = 7

x = 7 + 3

x = 10

Now, for the second equation, we also add 3 to both sides:

x - 3 = -7

x = -7 + 3

x = -4

The solutions to the equation |x - 3| = 7 are therefore x = 10 and x = -4. This reasoning aligns with the choice that provided these values, confirming it as the correct option. Understanding the absolute value concept is crucial as it leads to two potential scenarios—one reflecting a positive distance and the other a negative distance from the reference point.