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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Question
![### 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbadf131f-ca26-4f8e-953f-35e945c24016%2Fbc6b9ac5-69b8-4518-b289-5f4d4d33a967%2Fg7mdr5e_processed.jpeg&w=3840&q=75)
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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