Linear equation in one variable
- CBSE · NCERT Class 7 Part 2, Ch 7 Finding the Unknown
- CBSE · NCERT Class 9, Ch 2 Introduction to Linear Polynomials
A linear equation in one variable has one letter, with no squares or higher powers, such as 3x + 4 = 19.
An equation says two algebraic expressions are equal. The left side is the LHS and the right side is the RHS. "Linear" means the variable appears only as x, never as x² or x³. "One variable" means there is only one letter.
Solving it means finding the value that makes both sides equal. Think of a balance. Whatever you do to one side, you do to the other, and the balance holds.
A small example
Solve 3x + 4 = 19.
- Take 4 from both sides: 3x = 15.
- Divide both sides by 3: x = 5.
- Check in the first line: 3 × 5 + 4 = 19. Both sides match.
The check takes seconds and catches sign slips. For example, moving +4 across without changing it to -4 gives 3x = 23, and the check fails at once.
Why it matters later
Class 10 Chapter 3 solves a pair of linear equations in two variables. The substitution method turns the pair into a single equation in one variable. From there, every step is the one-variable solving shown above.
Sources
Facts last checked against these sources on 30 September 2026.
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