Absolute Value

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

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