Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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![### Solving Linear Equations
In this section, we will explore the steps used to solve a linear equation. Our example equation is:
\[ 2x + 8 = 20 \]
### Steps to Solve
1. **Step I:**
\[ 2x = 12 \]
2. **Step II:**
\[ x = 6 \]
### Question
Which property of equality makes Step I true?
### Answer Choices
- **A. Symmetric property of equality**
- **B. Division property of equality**
- **C. Reflexive property of equality**
- **D. Subtraction property of equality**
### Explanation of Steps
In Step I, to isolate the variable \( x \), the constant term 8 is subtracted from both sides of the equation:
\[ 2x + 8 - 8 = 20 - 8 \]
\[ 2x = 12 \]
This uses the **Subtraction property of equality**, which allows us to subtract equal values from both sides of an equation without changing the equality.
In Step II, both sides are divided by 2 to solve for \( x \):
\[ \frac{2x}{2} = \frac{12}{2} \]
\[ x = 6 \]
This uses the **Division property of equality**, which allows us to divide both sides of an equation by the same nonzero number.
### Correct Answer
The property that makes Step I true is:
- **D. Subtraction property of equality**
### Visual Aid
The interface shown includes navigation buttons and a percentage progress bar at the bottom right, which indicates the completion status of the test. The question presented is number 24 in the sequence.
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Transcribed Image Text:### Solving Linear Equations
In this section, we will explore the steps used to solve a linear equation. Our example equation is:
\[ 2x + 8 = 20 \]
### Steps to Solve
1. **Step I:**
\[ 2x = 12 \]
2. **Step II:**
\[ x = 6 \]
### Question
Which property of equality makes Step I true?
### Answer Choices
- **A. Symmetric property of equality**
- **B. Division property of equality**
- **C. Reflexive property of equality**
- **D. Subtraction property of equality**
### Explanation of Steps
In Step I, to isolate the variable \( x \), the constant term 8 is subtracted from both sides of the equation:
\[ 2x + 8 - 8 = 20 - 8 \]
\[ 2x = 12 \]
This uses the **Subtraction property of equality**, which allows us to subtract equal values from both sides of an equation without changing the equality.
In Step II, both sides are divided by 2 to solve for \( x \):
\[ \frac{2x}{2} = \frac{12}{2} \]
\[ x = 6 \]
This uses the **Division property of equality**, which allows us to divide both sides of an equation by the same nonzero number.
### Correct Answer
The property that makes Step I true is:
- **D. Subtraction property of equality**
### Visual Aid
The interface shown includes navigation buttons and a percentage progress bar at the bottom right, which indicates the completion status of the test. The question presented is number 24 in the sequence.
The options are presented as multiple-choice answers with radio buttons for selection, providing an intuitive way for students to select their answers.
**Powered by LinkIt!**
Providing accessible educational content is paramount for supporting student success.
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