Explanation

To solve absolute value questions, create an equation for each sign:

\(x + 3 = 12\) or \(x + 3 = -12\)

\(x = 9\) or \(x = -15\)

The only value of x that is a multiple of 5 is –15.
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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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Since the absolute value signs always output a positive value, the total amount within the absolute value signs must be either -12 or 12 in order for the equation to work.

For -12, we would need x = -15.

For 12, we would need x = 9.

Of these two, which is also a multiple of 5? -15 is.

Therefore, -15 is our answer.