Integers: Definition, Operations, and Worked Examples
Math Education6 min read
Math Education
6 min read
Algebra: Definition, Elements, and How to Work With It
Published: 12.08.2026·Updated: 12.08.2026
Putri Anggraini
Head of Math Program, Algonova
Algebra is the branch of mathematics that uses letters to stand for numbers we do not yet know, so relationships between numbers can be written down and solved in general.
The letter x is not a mysterious object. It is simply a temporary name for a number whose value is not yet known - much like calling someone the guest before learning their name.
Why Algebra Is Needed
Consider this problem: three books cost fifty-four thousand, what does one book cost. A primary child solves it by dividing. But if the problem becomes three books plus two pencils cost sixty thousand, where a pencil costs three thousand, dividing is no longer enough.
Algebra provides a way to write that relationship exactly as it is, then solve it step by step. This is why algebra is the gateway to almost all advanced mathematics.
The Elements of an Algebraic Expression
Take the expression 5x + 3y - 7.
| Element | Example here | Meaning |
|---|---|---|
| Variable | x and y | A letter standing for an unknown number |
| Coefficient | 5 and 3 | The number multiplying a variable |
| Constant | -7 | A number standing alone, with no variable |
| Term | 5x, 3y, and -7 | The parts separated by plus or minus signs |
The expression above has three terms. Counting terms is the first skill to master, because it determines which parts may be combined.
Like Terms
Two terms are alike if they have exactly the same variables, including the powers. Only like terms may be added or subtracted.
- 3x and 5x are alike, giving 8x.
- 3x and 5y are not alike and cannot be combined.
- 3x and 5x squared are not alike, despite sharing a letter.
A physical check: three pencils plus five pencils makes eight pencils, but three pencils plus five books stays three pencils and five books.
