SOLUTION: |x − 5| = 3

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Question 1210247: |x − 5| = 3
Answer by greenestamps(13289) About Me  (Show Source):
You can put this solution on YOUR website!


The equation abs%28x-5%29=3 means x-5 is equal to either 3 or -3. Solve the two equations separately.

x-5 = 3
x = 3+5 = 8

or

x-5 = -3
x = -3+5 = 2

ANSWERS: x = 8 or x = 2

That's the formal algebraic way to solve the problem.

There is another way to solve an absolute value equation like this that is usually easier (for me, at least) than the formal algebraic method.

The equation abs%28x-a%29=b can be interpreted as meaning "the difference between x and a is equal to b".

In this example, we have abs%28x-5%29=3, which we can interpret as saying "the difference between x and 5 is 3".

Then look on a number line to find all the numbers (there will be two of them) that are 3 away from 5.

3 to the right of 5 is 8; 3 to the left of 5 is 2. So (again, of course!) the solutions are x = 8 and x = 2.