Solve each absolute value equation.

Question

|x - 3| = 1

Okay here is what I did:

x - 3 = 1

x = 4 or x = -4

The book says {2,4}

I'm very lost. Can someone help me?

Answer 1

|x-3| = 1

Because of the absolute value, x-3 can equal 1 or - 1.

x-3 = 1 or x-3 = -1
x = ?

Answer 2

Ah I see, but I thought that an absolute value cannot equal a negative number. Maybe I'm just over thinking it.

Answer 3

To eliminate the absolute value you must consider the possibilities that the contents of the absolute value were positive or negative.

The absolute value cannot equal a negative - you will notice that while |x-3| = 1, x-3 = 1 or -1