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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![### Solving the Equation 5x + 2 = 2x + 17
Solve the equation \( 5x + 2 = 2x + 17 \) in two ways: with equations and with math drawings of a pan balance. Relate the two methods.
#### Method 1: Solving with Equations
1. Start with the given equation:
\[
5x + 2 = 2x + 17
\]
2. Subtract \( 2x \) from both sides to isolate terms with \( x \) on one side:
\[
5x - 2x + 2 = 2x - 2x + 17
\]
\[
3x + 2 = 17
\]
3. Subtract 2 from both sides:
\[
3x + 2 - 2 = 17 - 2
\]
\[
3x = 15
\]
4. Divide both sides by 3 to solve for \( x \):
\[
\frac{3x}{3} = \frac{15}{3}
\]
\[
x = 5
\]
So, the solution to the equation is \( x = 5 \).
#### Method 2: Solving with a Pan Balance Diagram
In a pan balance diagram, each side of the balance represents one side of the equation.
1. **Create the initial balance:**
- On the left side of the pan balance, represent \( 5x + 2 \).
- On the right side of the pan balance, represent \( 2x + 17 \).
2. **Balance the equation:**
- To balance the representation, remove \( 2x \) from both sides to simplify it, just as in the algebraic solution.
- This leaves \( 3x + 2 \) on the left pan and \( 17 \) on the right pan.
3. **Adjust for constants:**
- Subtract 2 units from both sides to maintain balance, resulting in \( 3x \) on the left pan and \( 15 \) on the right pan.
4. **Determine the variable value:**
- Each group of \( x \) on the left pan collectively balances with](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e4d9a92-7f6d-41e2-a11d-6abc746a28c0%2F72ba1b86-29a3-432b-8ddb-7fe248ff3fdb%2F5yk6pyy_processed.png&w=3840&q=75)
Transcribed Image Text:### Solving the Equation 5x + 2 = 2x + 17
Solve the equation \( 5x + 2 = 2x + 17 \) in two ways: with equations and with math drawings of a pan balance. Relate the two methods.
#### Method 1: Solving with Equations
1. Start with the given equation:
\[
5x + 2 = 2x + 17
\]
2. Subtract \( 2x \) from both sides to isolate terms with \( x \) on one side:
\[
5x - 2x + 2 = 2x - 2x + 17
\]
\[
3x + 2 = 17
\]
3. Subtract 2 from both sides:
\[
3x + 2 - 2 = 17 - 2
\]
\[
3x = 15
\]
4. Divide both sides by 3 to solve for \( x \):
\[
\frac{3x}{3} = \frac{15}{3}
\]
\[
x = 5
\]
So, the solution to the equation is \( x = 5 \).
#### Method 2: Solving with a Pan Balance Diagram
In a pan balance diagram, each side of the balance represents one side of the equation.
1. **Create the initial balance:**
- On the left side of the pan balance, represent \( 5x + 2 \).
- On the right side of the pan balance, represent \( 2x + 17 \).
2. **Balance the equation:**
- To balance the representation, remove \( 2x \) from both sides to simplify it, just as in the algebraic solution.
- This leaves \( 3x + 2 \) on the left pan and \( 17 \) on the right pan.
3. **Adjust for constants:**
- Subtract 2 units from both sides to maintain balance, resulting in \( 3x \) on the left pan and \( 15 \) on the right pan.
4. **Determine the variable value:**
- Each group of \( x \) on the left pan collectively balances with
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Where is the pan balance drawing to represent this equation and relate the math equations to the drawing?
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