Solve the following absolute value equation.
X-3| =- 14
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
• A.
the solution set is
(Simplify your answer. Use a comma to separate answers as needed.)
• B. The solution set is the empty set, (}.
To solve the absolute value equation X-3| =- 14, we have two cases to consider:
1. X-3 is nonnegative:
In this case, the absolute value equation simplifies to X-3 = -14. Solving for X, we add 3 to both sides: X = -11.
2. X-3 is negative:
In this case, the absolute value equation simplifies to -(X-3) = -14. Simplifying the equation inside the absolute value, we get -X+3 = -14. Solving for X, we subtract 3 from both sides: -X = -17. Multiplying by -1 to eliminate the negative sign, we get X = 17.
Therefore, the solution set is X = -11, 17.
Answer: A.