Solve the equation.
12 equals StartAbsoluteValue m plus 2 EndAbsoluteValue
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Part 1
Select the correct choice and, if necessary, fill in the answer box in your choice below.
A.
mequals
enter your response here
(Simplify your answer. Use a comma to separate answers as needed.)
B.
There is no solution.
To solve the equation 12 = |m + 2|, we need to consider two cases:
Case 1: m + 2 ≥ 0
In this case, |m + 2| simplifies to m + 2, so we have:
12 = m + 2
Subtracting 2 from both sides, we get:
10 = m
Case 2: m + 2 < 0
In this case, |m + 2| simplifies to -(m + 2), so we have:
12 = -(m + 2)
Multiplying both sides by -1, we get:
-12 = m + 2
Subtracting 2 from both sides, we get:
-14 = m
Therefore, the solutions to the equation are m = 10 and m = -14.
Answer: A. m = 10, -14