Stuart Griffin
03/22/2023 · Primary School
Solve the absolute value inequality. \[ |x-5| \geq 1 \] Select the correct answer below and, if necessary, fill in the answer box to complete \( y \) A. The solution set in interval notation is (Simplify your answer.) B. The solution set is \( \varnothing \).
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Solve the equation \( |x-5| \geq 1 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(\left|x-5\right|\geq 1\)
- step1: Separate into possible cases:
\(\begin{align}&x-5\geq 1\\&x-5\leq -1\end{align}\)
- step2: Solve the inequality:
\(\begin{align}&x\geq 6\\&x\leq 4\end{align}\)
- step3: Find the union:
\(x \in \left(-\infty,4\right]\cup \left[6,+\infty\right)\)
The solution to the absolute value inequality \( |x-5| \geq 1 \) is \( x \in (-\infty,4] \cup [6,+\infty) \).
Therefore, the correct answer is:
A. The solution set in interval notation is \( (-\infty,4] \cup [6,+\infty) \).
Quick Answer
A. The solution set in interval notation is \( (-\infty,4] \cup [6,+\infty) \).
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