Algebra Basics
8 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team
Algebra is arithmetic with letters. Instead of always working with specific numbers, you use symbols such as x to stand for an unknown or changing value, which lets you describe patterns and solve problems that would be awkward with numbers alone. This guide starts at the very beginning and builds up to solving equations.
Variables, constants and coefficients
A variable is a letter that stands for a number, like x or n. A constant is a fixed number, like 7. A coefficient is the number multiplying a variable: in 5x, the coefficient is 5. When there is no number written, the coefficient is 1, so x means 1x. Writing 3x means “3 times x”; the multiplication sign is left out.
Expressions versus equations
An expression is a combination of numbers and variables with no equals sign, such as 3x + 5. You can simplify or evaluate it, but you cannot “solve” it. An equation has an equals sign and states that two expressions are the same, such as 3x + 5 = 20. Solving an equation means finding the value of the variable that makes it true.
Evaluating: to evaluate 2x² − 3 when x = 5, substitute: 2 × 25 − 3 = 47. Remember the order of operations: exponents before multiplication.
Simplifying and the distributive property
Combine like terms: terms with the same variable part can be added. 3x + 2x = 5x, and 4y − y = 3y. But 3x + 2y cannot be combined.
Distribute: a number outside brackets multiplies every term inside. 3(x + 4) = 3x + 12, and −2(x − 5) = −2x + 10. Watch the signs: a negative multiplier flips every sign inside.
Solving equations: the balance idea
An equation is like a balanced scale. Do the same thing to both sides and it stays balanced. To solve 2x + 3 = 11:
- Subtract 3 from both sides: 2x = 8.
- Divide both sides by 2: x = 4.
- Check: 2(4) + 3 = 11 ✓.
Always undo operations in reverse order, working from the outside in. Try more in the equation solver.
Turning words into algebra
“A number tripled and then increased by 5 gives 26” becomes 3x + 5 = 26. Subtract 5: 3x = 21, so x = 7. To translate, pick a letter for the unknown, look for the operation words (“tripled” means × 3, “increased by” means + ) and write the equation.
| Words | Algebra |
|---|---|
| five more than a number | x + 5 |
| twice a number | 2x |
| a number decreased by 3 | x − 3 |
| the sum of a number and 7 is 15 | x + 7 = 15 |
Practice questions
Test yourself, then tap to check. Answers are calculated by the tools linked below.
- Solve 4x − 3 = x + 12.
Show answer
x: 5
- Calculate 7^4.
Show answer
7^4: 2,401
- Add 2/3 + 3/4.
Show answer
Simplified fraction: 17/12
Frequently asked questions
Why do we use letters in algebra?
Letters let us write rules that work for any number and represent unknown values we want to find.
What is the difference between an expression and an equation?
An expression has no equals sign and can be simplified. An equation states two expressions are equal and can be solved.
How do I check my answer?
Substitute it into the original equation. If both sides are equal, it is correct.
What should I learn after this?
Move on to <a href="/guides/algebraic-expressions">algebraic expressions</a> and <a href="/guides/linear-equations-guide">linear equations</a>.
Try it yourself
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