**Q: Solve the absolute value problem: |x/2 – 1/3| = 1**

A: Think of a number line… If I tell you to walk “10 units” on a number line, you can either walk 10 units to the right **or **10 units to the left… This is how we have to think of an absolute value. An absolute value measures distance — therefore, we must break an absolute value into 2 problem (as if you had walked right, which is the positive version, or as if you had walked left, which is the negative version):

So, get rid of the absolute value signs and split the problem into two:

x/2 – 1/3 = 1 **OR **x/2 – 1/3 = -1

Now, solve each problem separately:

x/2 – 1/3 = 1

Add 1/3 to each side:

x/2 – 1/3 + 1/3 = 1 + 1/3

x/2 = 4/3

Multiply both sides by 2:

2*x/2 = 2*4/3

2x/2 = 8/3

x = 8/3

Now solve the second problem

x/2 – 1/3 = -1

Add 1/3 to each side:

x/2 – 1/3 + 1/3 = -1 + 1/3

x/2 = -2/3

Multiply both sides by 2:

2*x/2 = 2*-2/3

2x/2 = -4/3

x = -4/3

So, **x = 8/3 or x = -4/3**