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|z| + 4 = 9 how do we solve this

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2 Answers

When solving an absolute value problem, I would isolate the absolute value until you get a form like 

|z| = some number

In this case this would invole subtracting 4 from both sides

|z| + 4 - 4 = 9 - 4  ==> |z| = 5

Now that we are here you have to remember that the absolute value is both the positive and negative value.  So:

|z| = 5  ==> z = 5 and z = -5

When you have an absolute value you need to solve the positive case and the negative case.

So |z| + 4 = 9 -> |z| = 5. (subtract 4 from both sides)

In the case z is negative –z=5, in the positive case z=5. So z = -5 or 5