Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Topic Video
Question
![**Translating Problems with Equations**
In this educational section, we will explore how to translate real-world problems into mathematical equations. We will use diagrams and graphical representations to illustrate these concepts.
**Diagram Explanation:**
The graph provided contains three distinct lines:
1. Two vertical lines extending infinitely in both upward and downward directions.
2. A diagonal line intersecting the two vertical lines.
**Labels on the Graph:**
- The horizontal distance between the vertical lines is represented by the expression \( x + 3 \).
- The diagonal line segment between the intersection points on the two vertical lines is represented by the expression \( 2x - 1 \).
**Interpreting the Diagram:**
1. **Vertical Lines:** These are likely representing two distinct positions or boundaries which we need to consider in our problem.
2. **Diagonal Line Segment:** This line represents a transformation or relationship between the values \( x + 3 \) and \( 2x - 1 \).
**Mathematical Translation:**
- We can set up an equation to find the values of \( x \), assuming these expressions are equal at the point of intersection.
For example, if we want to solve for \( x \):
\[ 2x - 1 = x + 3 \]
**Steps to Solve the Equation:**
1. Subtract \( x \) from both sides:
\[ 2x - x - 1 = 3 \]
\[ x - 1 = 3 \]
2. Add 1 to both sides:
\[ x = 4 \]
Through this process, we have determined the value of \( x \) which satisfies the given expressions in the diagram.
In summary, the diagram with the vertical and diagonal lines helps us visualize the relationships between different expressions and serve as a basis for translating and solving algebraic equations.
---
This example illustrates how visual aids can help in understanding complex mathematical problems and developing the skills to translate and solve equations from real-world scenarios.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5ca3db95-04f6-4873-a76d-c7ea06a8bcd8%2F5425fe97-7e45-4e3a-a21d-ad1a8e524998%2Fl5q8ggp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Translating Problems with Equations**
In this educational section, we will explore how to translate real-world problems into mathematical equations. We will use diagrams and graphical representations to illustrate these concepts.
**Diagram Explanation:**
The graph provided contains three distinct lines:
1. Two vertical lines extending infinitely in both upward and downward directions.
2. A diagonal line intersecting the two vertical lines.
**Labels on the Graph:**
- The horizontal distance between the vertical lines is represented by the expression \( x + 3 \).
- The diagonal line segment between the intersection points on the two vertical lines is represented by the expression \( 2x - 1 \).
**Interpreting the Diagram:**
1. **Vertical Lines:** These are likely representing two distinct positions or boundaries which we need to consider in our problem.
2. **Diagonal Line Segment:** This line represents a transformation or relationship between the values \( x + 3 \) and \( 2x - 1 \).
**Mathematical Translation:**
- We can set up an equation to find the values of \( x \), assuming these expressions are equal at the point of intersection.
For example, if we want to solve for \( x \):
\[ 2x - 1 = x + 3 \]
**Steps to Solve the Equation:**
1. Subtract \( x \) from both sides:
\[ 2x - x - 1 = 3 \]
\[ x - 1 = 3 \]
2. Add 1 to both sides:
\[ x = 4 \]
Through this process, we have determined the value of \( x \) which satisfies the given expressions in the diagram.
In summary, the diagram with the vertical and diagonal lines helps us visualize the relationships between different expressions and serve as a basis for translating and solving algebraic equations.
---
This example illustrates how visual aids can help in understanding complex mathematical problems and developing the skills to translate and solve equations from real-world scenarios.
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