What Is a Linear Equation?
An equation is a mathematical sentence that says two things are equal — there is always an equals sign (=) in the middle, balancing both sides.
A mathematical statement where two expressions are equal to each other, for example .
An equation where the variable has a power of 1 (no squared or cubed terms). In this subtopic, we work with linear equations in one variable (like ), which have a single solution — one value of that makes the equation true.
Did you know? The word linear comes from line. When a linear equation involves two variables (like ), its solutions form a straight line on a coordinate plane — but that is something you will explore in a later unit!
In this subtopic, we focus on linear equations in one variable (like ). These have a single numerical solution rather than producing a graph.
Think of an equation like a perfectly balanced set of scales — whatever you do to one side, you must do the same to the other side to keep it balanced.
Imagine a seesaw that is perfectly level. If you add weight to one side, it tips over. To keep it balanced, you must add the same weight to the other side. Equations work exactly the same way!
Key Vocabulary
Before solving equations, it helps to know the names of the parts you are working with.
A letter that represents a value that can change or is unknown, such as , , or .
The value you are trying to find by solving the equation.
A fixed number that does not change, such as or .
A single part of an expression — it can be a variable, a constant, or a combination of both (like ). Terms are separated by or signs.
In the equation :
- is a term (a combination of the constant 5 and the variable )
- and are constants
- is the variable (and the unknown we want to find)
10 more sections in this topic
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