Equations - Definition, Examples, Quiz, FAQ, Trivia
Learn to solve equations with simple explanations and practice activities
What is an Equation?
An equation is like a math sentence that shows two things are equal. It always has an equal sign (=) between two expressions. Equations help us find missing numbers and solve problems.
Think of equations like a balanced scale. Whatever is on the left side of the equal sign must have the same value as whatever is on the right side. Our job is to keep the scale balanced while we solve the equation!
Simple equation example:
Key Concept
An equation always has an equal sign (=) showing that two expressions have the same value.
Types of Equations
There are different kinds of equations. Here are some common ones you'll learn about:
1. Linear Equations: These make straight lines when graphed. They often look like:
Remember
The type of equation tells us about its graph. Linear makes straight lines, quadratic makes parabolas, and cubic makes S-curves.
Solving Equations
Solving an equation means finding the value of the variable (like x) that makes the equation true. We do this by keeping the equation balanced on both sides.
Equation Solving Steps
1. Simplify both sides of the equation
2. Move variables to one side
3. Use inverse operations
4. Check your solution
Step 1: Subtract 2 from both sides → 3x = 12
Step 2: Divide both sides by 3 → x = 4
Check: 3(4) + 2 = 12 + 2 = 14 ✓
| Equation | Solution | Explanation |
|---|---|---|
| x + 5 = 12 | x = 7 | Subtract 5 from both sides |
| 2x = 10 | x = 5 | Divide both sides by 2 |
| 3x - 4 = 11 | x = 5 | Add 4 to both sides, then divide by 3 |
| x/2 = 8 | x = 16 | Multiply both sides by 2 |
Solving Tip
Whatever you do to one side of the equation, you must do to the other side to keep it balanced!
Equation of a Line
The equation of a line is usually written as y = mx + b. This is called the slope-intercept form.
m is the slope - how steep the line is
b is the y-intercept - where the line crosses the y-axis
Example: y = 2x + 3
Slope (m) = 2 → For every 1 unit right, go up 2 units
Y-intercept (b) = 3 → Line crosses y-axis at (0, 3)
Graph Tip
To graph a line: 1) Plot the y-intercept, 2) Use the slope to find another point, 3) Draw the line through both points.
Equation Quiz
Test your knowledge with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about equations:
Math Trivia
Discover interesting facts about equations and mathematics:
Ancient Equations
The oldest known equation is from ancient Egypt around 1650 BC! It's written on the Rhind Papyrus and solves the equation x + x/7 = 19.
Einstein's Equation
Albert Einstein's famous equation E = mc² is one of the most recognized equations in the world. It shows that energy (E) and mass (m) are related.
Rocket Equations
NASA uses complex equations to launch rockets. The Tsiolkovsky rocket equation helps scientists calculate how much fuel is needed to reach space.
Longest Equation
The longest mathematical equation ever written has over 200 terabytes of data! It would take about 2.5 million books to print it all.
