What is a variable in algebra?

A variable is a letter (like x or n) that stands in place of an unknown number. It lets us write general rules and solve problems where the value is not yet known.

What is the difference between an expression and an equation?

An expression is a combination of numbers, variables, and operations (like 3x + 5). An equation has an equals sign and states that two expressions are equal (like 3x + 5 = 20).

How do you solve a two-step equation?

Undo the operations in reverse order (PEMDAS backwards). First undo addition or subtraction, then undo multiplication or division. Whatever you do to one side you must do to the other.

What does it mean to isolate the variable?

Isolating the variable means getting the letter (x, n, etc.) alone on one side of the equation, with its value on the other side. You do this by performing inverse operations.

Basic Algebra for Beginners: Variables, Equations & Solving

What You Will Learn

What variables and constants are

Difference between expressions and equations

The golden rule: balance both sides

Solve one-step equations (add, subtract, multiply, divide)

Solve two-step equations systematically

Write equations from word problems

Prerequisites

Comfortable with arithmetic operations (add, subtract, multiply, divide)
Basic understanding of percentages and decimals
Ability to work with fractions

What Is Algebra and Why Does It Matter?

Algebra is the branch of mathematics that uses letters — called variables — to represent unknown or changing quantities. Instead of asking "what is 5 + ? = 12?", algebra lets you write 5 + x = 12 and then solve for x using systematic rules.

Algebra shows up everywhere: calculating how long a road trip takes at a given speed, working out how much to tip, comparing phone plan prices, even coding a game. It is the language of logical reasoning applied to numbers.

Variable: A letter (x, y, n, t…) that represents an unknown number or a quantity that can change.
Constant: A fixed number that does not change (like 7, −3, or 100).
Expression: A combination of variables, constants, and operations — like 3x + 7. No equals sign.
Equation: A statement that two expressions are equal — like 3x + 7 = 22. Has an equals sign.

Expressions vs. Equations: Know the Difference

Mixing these two up causes endless confusion. Here is how to tell them apart instantly:

Expressions (No = sign)

4x + 3
2n − 7
5(y + 2)
x² + 3x

Equations (Has = sign)

4x + 3 = 19
2n − 7 = 11
5(y + 2) = 30
x + 8 = 15

You evaluate an expression (substitute a number for the variable). You solve an equation (find which value of the variable makes it true).

The Scale Analogy

Think of an equation as a perfectly balanced scale. Whatever operation you perform on the left side, you MUST perform the same operation on the right side. This is the golden rule of algebra — maintain the balance always.

One-Step Equations

A one-step equation needs only one operation to solve. The strategy is to use the inverse (opposite) operation to isolate the variable.

Addition equations — subtract to isolate

Example: Solve x + 9 = 17x + 9 = 17 x + 9 - 9 = 17 - 9 (subtract 9 from both sides) x = 8 Check: 8 + 9 = 17 ✓

Subtraction equations — add to isolate

Example: Solve n − 6 = 14n − 6 = 14 n − 6 + 6 = 14 + 6 (add 6 to both sides) n = 20 Check: 20 − 6 = 14 ✓

Multiplication equations — divide to isolate

Example: Solve 5x = 355x = 35 5x ÷ 5 = 35 ÷ 5 (divide both sides by 5) x = 7 Check: 5 × 7 = 35 ✓

Division equations — multiply to isolate

Example: Solve x/4 = 9x ÷ 4 = 9 (x ÷ 4) × 4 = 9 × 4 (multiply both sides by 4) x = 36 Check: 36 ÷ 4 = 9 ✓

Two-Step Equations

Two-step equations require two operations to solve. The trick is to work backwards — undo operations in the reverse order they were applied (PEMDAS in reverse: undo addition/subtraction first, then multiplication/division).

Example 1: Solve 3x + 5 = 20Step 1: Undo addition → subtract 5 from both sides 3x + 5 − 5 = 20 − 5 3x = 15 Step 2: Undo multiplication → divide both sides by 3 3x ÷ 3 = 15 ÷ 3 x = 5 Check: 3(5) + 5 = 15 + 5 = 20 ✓

Example 2: Solve 2n − 7 = 11Step 1: Undo subtraction → add 7 to both sides 2n − 7 + 7 = 11 + 7 2n = 18 Step 2: Undo multiplication → divide both sides by 2 2n ÷ 2 = 18 ÷ 2 n = 9 Check: 2(9) − 7 = 18 − 7 = 11 ✓

Example 3: Solve (x/3) + 4 = 10Step 1: Undo addition → subtract 4 x/3 + 4 − 4 = 10 − 4 x/3 = 6 Step 2: Undo division → multiply both sides by 3 (x/3) × 3 = 6 × 3 x = 18 Check: 18/3 + 4 = 6 + 4 = 10 ✓

Writing Equations from Word Problems

Translate the language of a problem into algebra by identifying the unknown (your variable), what you know (the constants), and the relationship between them.

Word problem: A number multiplied by 4, minus 3, equals 21. Find the number.Let n = the unknown number "Multiplied by 4": 4n "Minus 3": 4n − 3 "Equals 21": 4n − 3 = 21 Solve: 4n − 3 + 3 = 21 + 3 4n = 24 n = 6 Check: 4(6) − 3 = 24 − 3 = 21 ✓

⚠ 4 Most Common Algebra Mistakes

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Doing the operation to only one side. The golden rule: whatever you do to the left side, you must do to the right side. Every time. No exceptions.

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Undoing operations in the wrong order. Always undo addition/subtraction before multiplication/division when solving — work backwards through PEMDAS.

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Forgetting to check the answer. Substitute your answer back into the original equation. If both sides are equal, you have it right. If not, find the error.

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Thinking variables can only be x. Variables can be any letter. In science formulas you will see d = rt (distance = rate × time). In geometry, A = lw. Get comfortable with all letters.

Practice Problems

Solve: x + 14 = 31
x + 14 = 31 x = 31 − 14 x = 17 Check: 17 + 14 = 31 ✓
Solve: 6n = 54
6n = 54 n = 54 ÷ 6 n = 9 Check: 6 × 9 = 54 ✓
Solve: 4x − 3 = 25
Step 1: Add 3 to both sides 4x − 3 + 3 = 25 + 3 4x = 28 Step 2: Divide both sides by 4 x = 7 Check: 4(7) − 3 = 28 − 3 = 25 ✓
Solve: (n/5) + 6 = 14
Step 1: Subtract 6 from both sides n/5 = 8 Step 2: Multiply both sides by 5 n = 40 Check: 40/5 + 6 = 8 + 6 = 14 ✓
Word problem: Maria earns $8 per hour. After working some hours and spending $15 on lunch, she has $57 left. How many hours did she work?
Let h = hours worked Earnings: 8h After spending $15: 8h − 15 = 57 Solve: 8h − 15 + 15 = 57 + 15 8h = 72 h = 9 Answer: Maria worked 9 hours Check: 8(9) − 15 = 72 − 15 = 57 ✓

Trusted Learning Resources

Khan Academy — Algebra Foundations

Comprehensive free video series covering all beginner algebra topics with interactive exercises.

Math Is Fun — Introduction to Algebra

Friendly introductions to every algebra concept with worked examples and self-check quizzes.

Purple Math — Translating Word Problems

Expert guidance on converting word problems into algebraic equations — the trickiest algebra skill.

IXL — Algebra 1 Practice

Adaptive practice problems organized by skill level, with detailed explanations for every answer.

Continue the Math Fundamentals Series

← Previous: Percentages Explained — percent formulas are a great intro to equations with one unknown
← Also useful: Fractions for Beginners — algebra often involves fraction equations
→ Next: Geometry Essentials — apply algebra to calculate perimeter, area, and volume

Frequently Asked Questions

What is a variable in algebra?

A variable is a letter (like x or n) that stands in place of an unknown number. It lets you write general rules and solve problems where the value is not yet known.
What is the difference between an expression and an equation?

An expression is a combination of numbers, variables, and operations (like 3x + 5) with no equals sign. An equation has an equals sign and states that two expressions are equal (like 3x + 5 = 20).
How do you solve a two-step equation?

Work backwards through the order of operations. First undo addition or subtraction, then undo multiplication or division. Whatever you do to one side you must do to the other.
What does it mean to isolate the variable?

Isolating the variable means getting the letter alone on one side of the equation. You do this by performing inverse operations until only the variable remains on one side.

Basic Algebra for Beginners:Variables, Expressions & Equations