What is an Equation?
An equation is like a puzzle where you need to find a missing number. It's a statement that says two things are equal. For example, x + 5 = 12 means "some number plus 5 equals 12"—and your job is to work out what that number is.
The letter x (or any letter) stands for the missing number we need to find. This missing number is called the unknown.
Think of it like a seesaw at the playground. When both sides are balanced, they weigh the same. An equation works the same way—both sides of the equals sign must stay balanced.
The Golden Rule: Keep Both Sides Equal
The most important rule in solving equations is this: whatever you do to one side of the equation, you must do to the other side. This keeps everything balanced.
If we have x + 5 = 12, we need to get x on its own. To do this, we remove the 5 from the left side. But if we take away 5 from the left, we must also take away 5 from the right to keep it balanced:
x + 5 − 5 = 12 − 5
This simplifies to x = 7.
Think of it like sharing sweets between two friends. If one person loses 5 sweets, the other person must lose 5 sweets too, so it stays fair.
Steps to Solve Any Equation
Step 1: Identify what you need to get rid of on the side with the x.
Step 2: Do the opposite operation. If you're adding, subtract. If you're subtracting, add. If you're multiplying, divide. If you're dividing, multiply.
Step 3: Do that same operation to both sides of the equation.
Step 4: Simplify until x stands alone.
Step 5: Check your answer by putting the number back into the original equation.
Think of it like unwrapping a present. If something is added around your answer, you peel it away. If something is multiplied around it, you divide it away.
A Quick Example
Let's solve 3x = 15.
Here, x is being multiplied by 3. To undo multiplication, we divide both sides by 3:
3x ÷ 3 = 15 ÷ 3
This gives us x = 5.
To check: 3 × 5 = 15 ✓ Correct!
Once you practise these steps, solving equations becomes a satisfying puzzle where you're in control of finding the answer.