Question
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Tutor-Verified Answer
Answer
\( k = -7 \) or \( k = 21 \)
Solution
Solve the equation \( |k-7|=14 \).
Solve the equation by following steps:
- step0: Solve for \(k\):
\(\left|k-7\right|=14\)
- step1: Separate into possible cases:
\(\begin{align}&k-7=14\\&k-7=-14\end{align}\)
- step2: Solve the equation:
\(\begin{align}&k=21\\&k=-7\end{align}\)
- step3: Rewrite:
\(k_{1}=-7,k_{2}=21\)
The solutions to the equation \(|k-7|=14\) are \(k=-7\) and \(k=21\).
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Simplify this solution Mind Expander
To solve the equation \( |k-7|=14 \), we need to consider two scenarios due to the properties of absolute values. First, we set the expression inside the absolute value equal to 14: \( k-7=14 \), which leads to \( k=21 \). Secondly, we consider the negative case: \( k-7=-14 \), giving us \( k=-7 \). Thus, the solutions are \( k=21 \) and \( k=-7 \). Now, if you're in the middle of a math test and encounter an absolute value equation, remember: split it into its two cases! A common mistake is to forget to consider both the positive and negative scenarios, resulting in only one solution. Keep your cool, double-check your equations, and you’ll ace those absolute values!
