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Solve the equation | +6 - 4. The solutions are 1 = and 2 = where ₁ ≤ x2. This means x₁ is the smaller answer and 2 is the larger answer.

Solve the equation | +6 - 4. The solutions are 1 = and 2 = where ₁ ≤ x2. This means x₁ is the smaller answer and 2 is the larger 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 Equations **Problem:** Solve the equation \(|x + 6| = 4\). **Solution Steps:** The given equation involves an absolute value. We need to consider the definition of absolute value to solve for \(x\). The absolute value equation \(|x + 6| = 4\) means that: \(x + 6 = 4\) or \(x + 6 = -4\) Let's break this down into two separate equations to find the solutions for \(x\): 1. \(x + 6 = 4\) 2. \(x + 6 = -4\) **Solving the Equations:** 1. For \(x + 6 = 4\): \[ x = 4 - 6 \] \[ x = -2 \] 2. For \(x + 6 = -4\): \[ x = -4 - 6 \] \[ x = -10 \] **Solutions:** The solutions are \(x_1 = -10\) and \(x_2 = -2\), where \(x_1 \leq x_2\). This means: \[ x_1 = -10 x_2 = -2 \] So, \(x_1\) is the smaller answer and \(x_2\) is the larger answer.
Transcribed Image Text:### Solving Absolute Value Equations **Problem:** Solve the equation \(|x + 6| = 4\). **Solution Steps:** The given equation involves an absolute value. We need to consider the definition of absolute value to solve for \(x\). The absolute value equation \(|x + 6| = 4\) means that: \(x + 6 = 4\) or \(x + 6 = -4\) Let's break this down into two separate equations to find the solutions for \(x\): 1. \(x + 6 = 4\) 2. \(x + 6 = -4\) **Solving the Equations:** 1. For \(x + 6 = 4\): \[ x = 4 - 6 \] \[ x = -2 \] 2. For \(x + 6 = -4\): \[ x = -4 - 6 \] \[ x = -10 \] **Solutions:** The solutions are \(x_1 = -10\) and \(x_2 = -2\), where \(x_1 \leq x_2\). This means: \[ x_1 = -10 x_2 = -2 \] So, \(x_1\) is the smaller answer and \(x_2\) is the larger answer.
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