Question

During last year’s volleyball season, the coach concluded that the number of points you scored in each game could be given by the equation |x - 7| = 2. How many points did you score in each game ?

Answer 1

I would say 5 but I don’t understand the question much

Answer 2

The two solutions for x are x = 5 or x = 9.

We have some number x in which we subtract off 7. The result of this subtraction (x-7) is the value 2. If the result is negative, we flip it to positive. If the result is positive, we leave it alone. Absolute values are never negative because distance is never negative. Note how x = 5 is 2 units away from 7; similarly, x = 9 is also 2 units away from 7. Here's how you can solve for the two solutions

|x-7| = 2

x-7 = 2 or x-7 = -2

x-7+7 = 2+7 or x-7+7 = -2+7 .... add 7 to both sides

x = 9 or x = 5

x = 5 or x = 9

Therefore you could have scored 5 points or 9 points