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Solving Absolute Value Equations

Now...  What if we have to solve this guy?

| x + 5 | = 3

Think of this as

| blob | = 3

Remember the thing I told you to stick in your brain?

What can we say about the blob?

blob = -3 or blob = 3

Make sense?

I don't care what's inside those absolute value bars...  If it equals 3, then we have

| -3 | = 3 ... the blob is -3 ... or ... | 3 | = 3 ... the blob is 3

So, if the blob is  x + 5 ...

| x + 5 | = 3

| x + 5 | = -3 or | x + 5 | = 3

Now we just solve each of these:

x + 5 = -3 ... subtract 5 from both sides ... x = -8





x + 5 = 3 ... subtract 5 from both sides ... x = -2

Check them!

| x + 5 | = 3 ... x = -8
 

| -8 + 5 | = 3 ... | -3 | = 3 ... Yep!















| x + 5 | = 3 ... x = -2


| -2 + 5 | = 3 ... | 3 | = 3 ... Yep!

                                             { -2 , -8 }
            This is the set of the two things that work in our equation.