Equation and Its Roots
Understanding the foundation of algebraic problem-solving
What is an Equation with One Variable?
Definition: An equation with one variable is an equality containing one unknown (variable). It is also called an equation with one unknown.
Examples of Equations:
- 2x + 5 = 11 — linear equation
- x² − 4 = 0 — quadratic equation
- 3(x − 1) = x + 5 — equation with brackets
- x/2 = 7 — equation with fraction
Parts of an Equation
2x + 5
Left Side
(левая часть)
=
Equals Sign
(знак равенства)
11
Right Side
(правая часть)
An equation has two sides connected by the equals sign
What is a Root of an Equation?
Definition: A root of an equation is a value of the variable that makes the equation a true equality. It is also called a solution.
Example: Is x = 3 a root of 2x + 1 = 7?
Step 1: Substitute x = 3 into the equation
2(3) + 1 = 7
Step 2: Calculate the left side
6 + 1 = 7
7 = 7 ✓
Since left side equals right side, x = 3 IS a root!
Interactive visualization — available in the full lesson
The root is the \( x \)-value where the line \( y = 2x + 1 \) meets the line \( y = 7 \). At \( x = 3 \), both sides equal 7.