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Solve: |4x – 8| < 5 Give your answer as an interval. Check Answer

Solve: |4x – 8| < 5 Give your answer as an interval. Check Answer

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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## Solving Absolute Value Inequalities ### Problem Statement Solve the following inequality and provide your answer as an interval: \[ |4x - 8| < 5 \] ### Solution Steps 1. **Understanding the Inequality:** The expression \(|4x - 8| < 5\) implies that the absolute value of \(4x - 8\) is less than 5. This can be split into two separate inequalities: \[ -5 < 4x - 8 < 5 \] 2. **Solving the Inequalities:** - Separate the compound inequality into two parts: \[ 4x - 8 > -5 \quad \text{and} \quad 4x - 8 < 5 \] - Solve each part individually: - For \(4x - 8 > -5\): \[ 4x - 8 > -5 \\ 4x > -5 + 8 \\ 4x > 3 \\ x > \frac{3}{4} \\ x > 0.75 \] - For \(4x - 8 < 5\): \[ 4x - 8 < 5 \\ 4x < 5 + 8 \\ 4x < 13 \\ x < \frac{13}{4} \\ x < 3.25 \] 3. **Combining the Solutions:** - The solutions \(x > 0.75\) and \(x < 3.25\) combine to form the interval: \[ 0.75 < x < 3.25 \] 4. **Writing the Answer as an Interval:** - Express the solution in interval notation: \[ (0.75, 3.25) \] ### Final Step Enter the interval \((0.75, 3.25)\) in the answer box and click the "Check Answer" button. ### Interactive Elements - **Input Box:** - Placeholder text: "Enter interval here" - Input type: Text - **Button:** - Label: "Check Answer" This interactive problem helps in understanding how to
Transcribed Image Text:## Solving Absolute Value Inequalities ### Problem Statement Solve the following inequality and provide your answer as an interval: \[ |4x - 8| < 5 \] ### Solution Steps 1. **Understanding the Inequality:** The expression \(|4x - 8| < 5\) implies that the absolute value of \(4x - 8\) is less than 5. This can be split into two separate inequalities: \[ -5 < 4x - 8 < 5 \] 2. **Solving the Inequalities:** - Separate the compound inequality into two parts: \[ 4x - 8 > -5 \quad \text{and} \quad 4x - 8 < 5 \] - Solve each part individually: - For \(4x - 8 > -5\): \[ 4x - 8 > -5 \\ 4x > -5 + 8 \\ 4x > 3 \\ x > \frac{3}{4} \\ x > 0.75 \] - For \(4x - 8 < 5\): \[ 4x - 8 < 5 \\ 4x < 5 + 8 \\ 4x < 13 \\ x < \frac{13}{4} \\ x < 3.25 \] 3. **Combining the Solutions:** - The solutions \(x > 0.75\) and \(x < 3.25\) combine to form the interval: \[ 0.75 < x < 3.25 \] 4. **Writing the Answer as an Interval:** - Express the solution in interval notation: \[ (0.75, 3.25) \] ### Final Step Enter the interval \((0.75, 3.25)\) in the answer box and click the "Check Answer" button. ### Interactive Elements - **Input Box:** - Placeholder text: "Enter interval here" - Input type: Text - **Button:** - Label: "Check Answer" This interactive problem helps in understanding how to
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