For each of the problems below, use the strategies of removing zeros or adding/removing balanced sets so that all the x-variables are on one side and the unit tiles are on the other. Record your steps.
For each of the problems below, use the strategies of removing zeros or adding/removing balanced sets so that all the x-variables are on one side and the unit tiles are on the other. Record your steps.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Using legal moves, how do I move so that all x variable are on one side and unit tiles are on the other?

Transcribed Image Text:**Title: Solving Algebraic Equations with Visual Aids**
**Problem Instructions:**
For each of the problems below, use the strategies of removing zeros or adding/removing balanced sets so that all the x-variables are on one side and the unit tiles are on the other. **Record your steps.**
**Problem 7:**
- **Left Side:**
- Contains a plus sign with one large rectangle labeled 'x'.
- Below the line is a section with two small squares and a large rectangle labeled 'x' with a minus sign.
- **Right Side:**
- Contains a plus sign with three large rectangles labeled 'x' and two small squares.
- Below the line is a large rectangle labeled '-x'.
- **Question:** Which side is greater?
**Problem 8:**
- **Left Side:**
- Contains a plus sign with four large rectangles labeled 'x' and one small square.
- Below the line is a section with two small squares and a large rectangle labeled '-x'.
- **Right Side:**
- Contains a plus sign with three large rectangles labeled 'x' and three small squares.
- Below the line is a large rectangle labeled 'x'.
- **Question:** Which side is greater?
**Instructions for Solving:**
1. **Identify the x-variables and unit tiles on each side.**
- Move all x-variables to one side of the equation by adding or subtracting them from both sides.
- Move all unit tiles to the opposite side.
2. **Simplify the equations by canceling out pairs of 'x' or unit tiles that appear on both sides.**
3. **Determine which side is greater by comparing the quantities of remaining 'x' tiles and unit tiles.**
**Reflect and Write Down:**
- After rearranging the variables and unit tiles, record the steps taken for each problem.
- Analyze which side has a greater value after simplification.
Use these strategies to better understand balancing equations and the concept of isolating variables.
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