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Score: \( 1 / 4 \) Penalty: 0.5 off Question Solve the following inequality algebraically. \[ |x+8|<5 \] Answer Attempt s out of 10

Ask by Clark Reese. in the United States
Feb 19,2025

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Answer

The solution to the inequality \( |x+8|<5 \) is \(-13 < x < -3\).

Solution

Solve the equation \( |x+8|<5 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(\left|x+8\right|<5\) - step1: Separate into possible cases: \(\left\{ \begin{array}{l}x+8<5\\x+8>-5\end{array}\right.\) - step2: Solve the inequality: \(\left\{ \begin{array}{l}x<-3\\x>-13\end{array}\right.\) - step3: Find the intersection: \(-13

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Beyond the Answer

To solve the inequality \( |x+8| < 5 \), we start by recognizing that this absolute value inequality represents two separate cases. 1. **First case**: \[ x + 8 < 5 \] This simplifies to \( x < -3 \). 2. **Second case**: \[ x + 8 > -5 \] This simplifies to \( x > -13 \). Now, we need to combine the results from both cases to find the solution set. Therefore, the results give us the interval: \[ -13 < x < -3 \] So the final solution to the inequality \( |x+8| < 5 \) is: \[ x \in (-13, -3) \] Feel free to ask if you have any questions or need clarification!

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