You have probably seen an equation like x + 5 = 12 and wondered — what is x? Is it a letter? A mystery? A trick? It is none of those things. A variable is simply a placeholder for a number you do not know yet. Once that clicks, all of early algebra starts to make sense.
What is a Variable?
Think of a variable as a labelled box. The box has a name — usually x, but it could be y, n, or any letter — and it holds exactly one number. Your job in an equation is to figure out which number belongs in that box.
Definition: Variable
Variables can hold any kind of number — whole numbers, fractions, negative numbers, even zero. The letter itself has no value until you solve the equation.
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Book free demoThe Balance Principle — The Most Important Idea in Algebra
An equation is like a perfectly balanced scale. The equals sign = means both sides weigh exactly the same. If you add weight to one side, you must add the same weight to the other — or the scale tips and the equation breaks.
How to Solve a Simple Equation — Step by Step
The goal when solving is to get the variable alone on one side of the equals sign. We call this isolating the variable. Here are the most common types you will see in Grade 7-8.
Type 1: One-step equations
Solve: x + 5 = 12
Identify what is being added to x
Subtract 5 from both sides
Check your answer
Solve: 3x = 18
Identify what is multiplying x
Divide both sides by 3
Check your answer
Type 2: Two-step equations
Two-step equations combine two operations. The strategy is to undo them in reverse order — first undo the addition or subtraction, then undo the multiplication or division.
Solve: 2x + 6 = 14
Subtract 6 from both sides (undo the + 6 first)
Divide both sides by 2 (undo the × 2)
Check your answer
Solve: x/3 − 2 = 7
Add 2 to both sides
Multiply both sides by 3
Check your answer
Variables on Both Sides
Sometimes x appears on both sides of the equation. The trick is to collect all the variable terms on one side first.
Solve: 5x − 3 = 3x + 7
Move variable terms to the left by subtracting 3x from both sides
Add 3 to both sides
Divide both sides by 2
Check
Quick-Reference: Undoing Operations
| If x has… | Undo it by… |
|---|---|
| something added | subtracting the same amount |
| something subtracted | adding the same amount |
| something multiplied | dividing by the same number |
| something divided | multiplying by the same number |
Practice Problems
- 1
Solve: x − 9 = 14
Hint: Add 9 to both sides.
- 2
Solve: 4x = 36
Hint: Divide both sides by 4.
- 3
Solve: 3x + 5 = 20
Hint: Subtract 5 first, then divide.
- 4
Solve: x/4 + 1 = 6
Hint: Subtract 1 first, then multiply by 4.
- 5
Solve: 6x − 4 = 2x + 12
Hint: Move the x terms to one side first.
Ready for the next level?
Once you are comfortable solving linear equations, the natural next step is working with two variables simultaneously — called a system of equations. After that, quadratic equations open up a whole new set of problem types.
If you would like one-on-one help building these foundations, book a free demo session and we will assess exactly where you are and what to work on next.
