Which equation can you solve? Explain how you can determine which can be solved. a) |x-3|=7 or b) |x-3|=-7

Answer 1

a) can be solved since it can either be x-3 = 7 or x-3 =-7, making x = 10 or x = -4.

b) Can't be solved because the definition of absolute value only produces a positive value. -7 is not a positive number.

Answer 2

Absolute value is distance from zero, and we measure distance using positive numbers. Both ten and negative ten are ten away from zero, so they both have an absolute value of ten, for example.

In your problem, in A, you'll have 2 answers because x - 3 could equal 7 or -7, as they both have an absolute value of 7, but B has no solution, because nothing has a negative absolute value.