Davies May
05/24/2023 · Middle School
Solve the inequality involving absolute value. Write your final answer in interval notation. (If the solution set is empty, enter EMPTY or \( \emptyset \).) \[ |5 x-1|>14 \]
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Step-by-step Solution
We start by isolating the absolute value on one side of the inequality:
\begin{align*}
|5x-1| &> 14 \\
5x-1 &> 14 \quad \text{or} \quad 5x-1 < -14 && \text{by definition of absolute value} \\
5x &> 15 \quad \text{or} \quad 5x < -13 \\
x &> 3 \quad \text{or} \quad x < -\frac{13}{5}
\end{align*}
Therefore, the solution set is $(-\infty, -\frac{13}{5}) \cup (3, \infty)$. In interval notation, we write this as $\boxed{(-\infty, -\frac{13}{5}) \cup (3, \infty)}$.
Quick Answer
The solution set is $(-\infty, -\frac{13}{5}) \cup (3, \infty)$.
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