Linear Equations in One Variable is part of the Class 9 Mathematics syllabus for the AISSEE (Sainik School) entrance exam, where Maths carries 200 of 400 marks (50 questions × 4 marks), and for the RMS CET Class 9 paper. AISSEE 2027 is on Sunday, 31 January 2027, with no negative marking.
What Is a Linear Equation?
A linear equation in one variable has one unknown (such as x) whose highest power is 1, for example 3x + 5 = 20. Solving it means finding the value of x that makes both sides equal.
Golden Rules
Whatever you do to one side, do to the other side.
Transposing: a term moving across the "=" sign changes its sign (+ becomes −, × becomes ÷).
Remove brackets first, then collect x-terms on one side and numbers on the other.
For fractions, multiply both sides by the LCM of the denominators.
Always check your answer by putting it back in the equation.
Solved Examples
3x + 5 = 20 → 3x = 15 → x = 5
x/2 + 3 = 7 → x/2 = 4 → x = 8
2(x − 3) = x + 4 → 2x − 6 = x + 4 → x = 10
x/3 − x/4 = 2 → multiply by 12: 4x − 3x = 24 → x = 24
Consecutive numbers: the sum of two consecutive numbers is 41. x + (x + 1) = 41 → x = 20, so the numbers are 20 and 21.
Ages: a father is 3 times as old as his son. In 10 years he will be twice as old. Let the son be s: 3s + 10 = 2(s + 10) → s = 10. Son 10 years, father 30 years.
Word-Problem Method
Let the unknown be x and write what x stands for.
Turn each sentence into an expression.
Form the equation and solve it.
Answer the actual question (with units) and check it.
Common Mistakes
Forgetting to change the sign when transposing.
Multiplying only one term by the LCM instead of every term.
Stopping at x when the question asks for something else (such as "the larger number").
Practise and Revise
Linear Equations MCQs — 10 questions with answers and explanations
Free AISSEE / RMS Mock Test
Enunciate Academy runs online coaching for Sainik School, RMS, Navodaya and RIMC entrance exams for Class 4 to 9 students across Andhra Pradesh and Telangana. Message us on WhatsApp (94924 44498) to get a free mock test, or see the Spark batch details.
