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📐 Algebra Tutorial

Discover the power of variables and equations

Introduction to Algebra

What is Algebra?

Algebra is like arithmetic with a twist - we use letters (called variables) to represent unknown numbers. Think of it as solving puzzles!


Key Concepts:

  • Variables - Letters that represent unknown numbers (like x, y, z)
  • Equations - Mathematical statements that two things are equal
  • Solving - Finding the value of the variable
  • Balance - Whatever you do to one side, do to the other

Real-world Examples:

🎂 Age Problem: "I am 5 years older than my sister. If I am 17, how old is my sister?"

My age = Sister's age + 5

17 = x + 5

🛒 Shopping: "I bought 3 identical items and spent $15. How much did each item cost?"

3 × price = $15

3x = 15

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Understanding Variables

A variable is like a box that can hold different numbers. We use letters like x, y, or n to represent these unknown values.

Variable Examples:

If x = 5, then:

  • x + 3 = 5 + 3 = 8
  • 2x = 2 × 5 = 10
  • x - 1 = 5 - 1 = 4

Practice: Substitute the Variable

If x = 7, what is 3x + 4?


Simple Equations

An equation is like a balance scale. Whatever you do to one side, you must do to the other side to keep it balanced.

Solving: x + 5 = 12

x + 5
=
12
Step 1: Subtract 5 from both sides
x + 5 - 5 = 12 - 5
Step 2: Simplify
x = 7

Solve the Equation

x + 8 = 15

What is x?


Two-Step Equations

Some equations require two steps to solve. Remember: undo operations in reverse order!

Solving: 2x + 3 = 11

Step 1: Subtract 3 from both sides
2x + 3 - 3 = 11 - 3
2x = 8
Step 2: Divide both sides by 2
2x ÷ 2 = 8 ÷ 2
x = 4

Solve the Two-Step Equation

3x - 6 = 15

What is x?


Word Problems

Turn real-world situations into equations. Look for keywords and identify what the variable represents.

Example: Age Problem

"Sarah is 3 years older than twice her brother's age. If Sarah is 17, how old is her brother?"

Step 1: Define the variable
Let x = brother's age
Step 2: Write the equation
2x + 3 = 17
Step 3: Solve
2x = 14
x = 7

Word Problem Challenge

"A number increased by 12 equals 25. What is the number?"

What is the number?


🎯 Algebra Practice Test

Test your algebra skills with a variety of problems!

Question 1 of 5

Ready? Click 'Start Test' to begin!