Question
Solve: \( |2 x+1|>8 \) Give your answer as an interval. Note: Type oo for the infinity symbol \( \infty \) and
Ask by Watson Erickson. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x \in (-\infty, -\frac{9}{2}) \cup (\frac{7}{2}, \infty) \)
Solution
Solve the equation \( |2x+1|>8 \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(\left|2x+1\right|>8\)
- step1: Separate into possible cases:
\(\begin{align}&2x+1>8\\&2x+1<-8\end{align}\)
- step2: Solve the inequality:
\(\begin{align}&x>\frac{7}{2}\\&x<-\frac{9}{2}\end{align}\)
- step3: Find the union:
\(x \in \left(-\infty,-\frac{9}{2}\right)\cup \left(\frac{7}{2},+\infty\right)\)
The solution to the inequality \(|2x+1|>8\) is \(x \in (-\infty, -\frac{9}{2}) \cup (\frac{7}{2}, \infty)\).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve the inequality \( |2x + 1| > 8 \), we can break it down into two separate cases: 1. \( 2x + 1 > 8 \) 2. \( 2x + 1 < -8 \) **Case 1:** \[ 2x + 1 > 8 \] Subtracting 1 from both sides gives: \[ 2x > 7 \] Dividing both sides by 2 results in: \[ x > \frac{7}{2} \] **Case 2:** \[ 2x + 1 < -8 \] Subtracting 1 from both sides gives: \[ 2x < -9 \] Dividing both sides by 2 results in: \[ x < -\frac{9}{2} \] Combining these results, the solution to the inequality \( |2x + 1| > 8 \) in interval notation is: \[ (-\infty, -\frac{9}{2}) \cup (\frac{7}{2}, \infty) \]
