Vaughan Bush
05/26/2023 · High School
Select the correct answer. Solve the following equation. \[ \begin{array}{l}|x|+8=17 \\ \text { A. } x=9 \text { or } x=-9 \\ \text { B. } x=25 \text { or } x=-25 \\ \text { C. } x=25 \text { or } x=-9 \\ \text { D. } x=-25 \text { or } x=-9\end{array} \]
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Step-by-step Solution
Solve the equation \( |x|+8=17 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\left|x\right|+8=17\)
- step1: Move the constant to the right side:
\(\left|x\right|=17-8\)
- step2: Subtract the numbers:
\(\left|x\right|=9\)
- step3: Separate into possible cases:
\(\begin{align}&x=9\\&x=-9\end{align}\)
- step4: Rewrite:
\(x_{1}=-9,x_{2}=9\)
The solution to the equation \( |x|+8=17 \) is \( x=-9 \) or \( x=9 \).
Therefore, the correct answer is A. \( x=9 \) or \( x=-9 \).
Quick Answer
The correct answer is A. \( x=9 \) or \( x=-9 \).
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