If | x + 3| = 12 and x is a multiple of 5, what is the value of x ?

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There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k and/or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

So, if |x + 3| = 12, then EITHER x + 3 = 12 OR x + 3 = -12
If x + 3 = 12, then x = 9
If x + 3 = -12, then x = -15

So, x = 9 or x = -15
Since we're told x is a multiple of 5, we can conclude that x = -15
A quick check will verify that this solution is correct.

Answer:

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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