### Solving Linear EquationsIn this section, we will explore the steps used to solve a linear equation. Our example equation is:\[ 2x + 8 = 20 \]### Steps to Solve1. **Step I:**\[ 2x = 12 \]2. **Step II:**\[ x = 6 \]### QuestionWhich 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 StepsIn 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 AnswerThe property that makes Step I true is:- **D. Subtraction property of equality**### Visual AidThe 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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Answered: The steps used to solve the equation 2x…

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The steps used to solve the equation 2x + 8 = 20 for x are shown below. 2x + 8 = 20 %3D Step I: 2x = 12 Step II x = 6

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.

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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.

The options are presented as multiple-choice answers with radio buttons for selection, providing an intuitive way for students to select their answers.

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