Solving Equations with Variables on Both Sides
In this lesson, we will learn how to solve equations that have variables on both sides of the equation. These types of equations require you to collect all the variable terms on one side and all the constant terms on the other side before solving for the variable.
Outline
- Introduction to Equations with Variables on Both Sides
- Key Steps in Solving These Equations
- Examples
- Exercises with Solutions
- Homework
- Revision Section
- Contact Us for Tutoring
Examples of Solving Equations with Variables on Both Sides
Example 1:
Solve: \(3x + 5 = 2x + 9\)
Step 1: Subtract \(2x\) from both sides: \(x + 5 = 9\)
Step 2: Subtract 5 from both sides: \(x = 4\)
Example 2:
Solve: \(4x - 7 = 2x + 3\)
Step 1: Subtract \(2x\) from both sides: \(2x - 7 = 3\)
Step 2: Add 7 to both sides: \(2x = 10\)
Step 3: Divide by 2: \(x = 5\)
Example 3:
Solve: \(5x + 2 = 3x + 14\)
Step 1: Subtract \(3x\) from both sides: \(2x + 2 = 14\)
Step 2: Subtract 2 from both sides: \(2x = 12\)
Step 3: Divide by 2: \(x = 6\)
Example 4:
Solve: \(6x - 4 = 4x + 8\)
Step 1: Subtract \(4x\) from both sides: \(2x - 4 = 8\)
Step 2: Add 4 to both sides: \(2x = 12\)
Step 3: Divide by 2: \(x = 6\)
Example 5:
Solve: \(7x + 3 = 5x + 11\)
Step 1: Subtract \(5x\) from both sides: \(2x + 3 = 11\)
Step 2: Subtract 3 from both sides: \(2x = 8\)
Step 3: Divide by 2: \(x = 4\)
Example 6:
Solve: \(8x - 6 = 6x + 10\)
Step 1: Subtract \(6x\) from both sides: \(2x - 6 = 10\)
Step 2: Add 6 to both sides: \(2x = 16\)
Step 3: Divide by 2: \(x = 8\)
Exercises
Practice Problems:
- Solve: \(3x + 4 = 2x + 10\)
- Solve: \(5x - 7 = 3x + 9\)
- Solve: \(6x + 8 = 4x + 20\)
- Solve: \(7x - 5 = 5x + 13\)
- Solve: \(9x + 2 = 7x + 18\)
- Solve: \(4x + 10 = 3x + 14\)
Solutions:
1. \(x = 6\)
2. \(x = 8\)
3. \(x = 6\)
4. \(x = 9\)
5. \(x = 8\)
6. \(x = 4\)
Homework
Homework Problems:
- Solve: \(2x + 3 = x + 10\)
- Solve: \(4x - 6 = 2x + 8\)
- Solve: \(5x + 7 = 3x + 21\)
- Solve: \(8x - 9 = 6x + 15\)
- Solve: \(7x + 2 = 4x + 20\)
Revision Section
To revise this topic, remember the key steps:
- Get all variable terms on one side of the equation.
- Get all constant terms on the opposite side.
- Simplify and solve for the variable.
Watch the Video Tutorial
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