💡 The Big Idea
Every one-step equation has a variable (like x) with one operation applied to it. Your job is to undo that operation using its inverse — while keeping both sides of the equation perfectly balanced. Once you isolate x, you have your answer!
A one-step equation is an algebraic equation where you need to perform exactly one inverse operation to find the value of the unknown variable (usually x).
Goal: Isolate x — get x by itself on one side of the equation.
Look at what's being done to x: added? subtracted? multiplied? divided?
Example: in x + 7 = 12, the operation is addition (+7).
Undo the operation by applying its opposite to both sides of the equals sign.
Example: undo +7 by subtracting 7 from both sides.
After the inverse operation, x stands alone with its value.
Example: x = 12 − 7 = 5
| Type | Example | Inverse Operation | Answer |
|---|---|---|---|
| Addition | x + 7 = 12 | Subtract 7 | x = 5 |
| Subtraction | x − 3 = 10 | Add 3 | x = 13 |
| Multiplication | 4x = 20 | Divide by 4 | x = 5 |
| Division | x/3 = 6 | Multiply by 3 | x = 18 |
An inverse operation is the opposite of a given operation. Just like multiplication undoes division, subtraction undoes addition. Use the inverse to isolate x!
Operation on x: +7 (addition)
Inverse: subtract 7 from both sides
x + 7 − 7 = 12 − 7 → x = 5
Operation on x: × 4 (multiplication)
Inverse: divide by 4 on both sides
4x ÷ 4 = 20 ÷ 4 → x = 5
What is the inverse operation for x − 3 = 10? (What undoes subtraction?)
Whatever you do to one side, you MUST do to the other side.
This keeps the equation balanced and true. If you subtract 7 from the left, you must subtract 7 from the right too!
🔑 Why This Works
Think of an equation as a perfectly balanced scale. If you take weight off one side, the scale tips. To keep it balanced, you must take the same amount off both sides. Equations work the same way — always apply operations to both sides equally!
If the equation has x + a = b, subtract a from both sides to isolate x:
x = b − a
5 + 7 = 12 ✅
Solve x + 9 = 15. (What do you subtract from both sides?)
If the equation has x − a = b, add a to both sides:
x = b + a
13 − 3 = 10 ✅
Solve x − 8 = 5. (What do you add to both sides?)
If the equation has a·x = b, divide both sides by a:
x = b ÷ a
Note: 4x means 4 × x — the number written next to x is always multiplying it!
Solve 6x = 42. (Divide both sides by 6 — what do you get?)
Addition: a=7, b=12 → should get x=5 | Subtraction: a=3, b=10 → should get x=13 | Multiplication: a=4, b=20 → should get x=5