🎓 Mini-Lesson: Introduction to Algebra
What is Algebra?
Algebra is a branch of mathematics where we use letters (called variables) to represent unknown numbers. These letters can stand for any value, and we use algebra to find out what they are!
Simplifying Expressions
Collecting Like Terms
Like terms have the same variable raised to the same power. We can add and subtract like terms.
Example 1: Simplify 3x + 5x
3x + 5x = 8x
Think of it as: 3 apples + 5 apples = 8 apples
Example 2: Simplify 7y - 2y + 4
- Identify like terms: 7y and -2y are like terms (both have y)
- Combine them: 7y - 2y = 5y
- Keep the constant: +4
- Final answer: 5y + 4
Example 3: Simplify 4x + 3y - x + 2y
- Group like terms: (4x - x) + (3y + 2y)
- Simplify each: 3x + 5y
- Final answer: 3x + 5y
Solving Linear Equations
Finding the Value of x
To solve equations, we need to get the variable on its own by doing the same thing to both sides.
Example 4: Solve x + 7 = 15
- We want x on its own
- Subtract 7 from both sides: x + 7 - 7 = 15 - 7
- Simplify: x = 8
Example 5: Solve 3x = 21
- We want x on its own
- Divide both sides by 3: 3x ÷ 3 = 21 ÷ 3
- Simplify: x = 7
Example 6: Solve 2x + 5 = 17
- Subtract 5 from both sides: 2x + 5 - 5 = 17 - 5
- Simplify: 2x = 12
- Divide both sides by 2: 2x ÷ 2 = 12 ÷ 2
- Final answer: x = 6
🔑 Golden Rules of Algebra:
- Like terms only: You can only add/subtract terms with the same variable (3x + 2x ✓, but not 3x + 2y)
- Balance the equation: Whatever you do to one side, do to the other
- Opposite operations: Use subtraction to undo addition, division to undo multiplication
- Work systematically: Deal with addition/subtraction first, then multiplication/division
💡 Remember: Letters are just numbers in disguise. Treat them the same way you'd treat numbers!
✏️ Practice Questions
Simplify the expressions or solve the equations. Write your answers carefully!