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Solve | | - 3x +8 24

Solve | | - 3x +8 24

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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The image displays a mathematical inequality problem using absolute values. The instruction is: "Solve: \(|-3x + 8| \geq 4\)" This means you need to find the values of \(x\) for which the expression \(-3x + 8\) inside the absolute value bars is either greater than or equal to 4, or less than or equal to -4. Here's how you might proceed to solve it: 1. **Split the inequality into two cases:** - Case 1: \(-3x + 8 \geq 4\) - Case 2: \(-3x + 8 \leq -4\) 2. **Solve each case separately:** **Case 1:** - Subtract 8 from both sides: \(-3x \geq -4\) - Divide by -3 and reverse the inequality sign: \(x \leq \frac{4}{3}\) **Case 2:** - Subtract 8 from both sides: \(-3x \leq -12\) - Divide by -3 and reverse the inequality sign: \(x \geq 4\) 3. **Combine the solutions:** - The solution is the union of both inequalities: \(x \leq \frac{4}{3}\) or \(x \geq 4\). This represents the set of all real numbers \(x\) such that \(x\) is less than or equal to \(\frac{4}{3}\) or greater than or equal to 4.
Transcribed Image Text:The image displays a mathematical inequality problem using absolute values. The instruction is: "Solve: \(|-3x + 8| \geq 4\)" This means you need to find the values of \(x\) for which the expression \(-3x + 8\) inside the absolute value bars is either greater than or equal to 4, or less than or equal to -4. Here's how you might proceed to solve it: 1. **Split the inequality into two cases:** - Case 1: \(-3x + 8 \geq 4\) - Case 2: \(-3x + 8 \leq -4\) 2. **Solve each case separately:** **Case 1:** - Subtract 8 from both sides: \(-3x \geq -4\) - Divide by -3 and reverse the inequality sign: \(x \leq \frac{4}{3}\) **Case 2:** - Subtract 8 from both sides: \(-3x \leq -12\) - Divide by -3 and reverse the inequality sign: \(x \geq 4\) 3. **Combine the solutions:** - The solution is the union of both inequalities: \(x \leq \frac{4}{3}\) or \(x \geq 4\). This represents the set of all real numbers \(x\) such that \(x\) is less than or equal to \(\frac{4}{3}\) or greater than or equal to 4.
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