Linear Expressions
SSC GD Exam Preparation - Quantitative Aptitude
A linear expression is an algebraic expression in which the degree of the variable is 1. It contains terms of the form ax + b, where a and b are constants.
Examples:
2x + 3
✅ Linear
5y - 7
✅ Linear
x² + 3x + 2
❌ Not linear (degree 2)
🔹 1. General Form
ax + b
x = variable
a, b = constants
a ≠ 0
🔹 2. Operations on Linear Expressions
a. Addition
(2x + 3) + (5x - 7) = 7x - 4
b. Subtraction
(6x + 5) - (3x - 2) = 3x + 7
c. Multiplication by a constant
k(3x + 4) = 3kx + 4k
d. Simplification
Combine like terms:
3x + 2 + 5x - 4 = 8x - 2
🔹 3. Solving Linear Equations from Expressions
Example:
Convert expression to equation if needed:
2x + 5 = 11
⇒ 2x = 6
⇒ x = 3
🧠 Practice Section: 15 Questions (With Answers)
Each Q followed by its Answer (SSC style). Click on "View Answer" to check your understanding.
Q1. Simplify 3x + 5 + 7x - 2
View Answer
10x + 3
Q2. Simplify 6y - 3 + 2y + 7
View Answer
8y + 4
Q3. Simplify 4a + 5 - 2a + 3
View Answer
2a + 8
Q4. Multiply 3(2x + 4)
View Answer
6x + 12
Q5. Multiply 5(3y - 2)
View Answer
15y - 10
Q6. Solve 2x + 5 = 13
View Answer
2x = 8 ⇒ x = 4
Q7. Solve 3y - 7 = 8
View Answer
3y = 15 ⇒ y = 5
Q8. Subtract (5x + 6) - (3x - 2)
View Answer
2x + 8
Q9. Simplify 7a + 4 - 2a - 5
View Answer
5a - 1
Q10. Multiply -2(3x - 5)
View Answer
-6x + 10
Q11. Solve 4x + 9 = 25
View Answer
4x = 16 ⇒ x = 4
Q12. Simplify 3x + 2 + 5x - 7 + x + 6
View Answer
9x + 1
Q13. Multiply 2(4y + 3) - 5
View Answer
8y + 6 - 5 = 8y + 1
Q14. Solve 6a - 3 = 9
View Answer
6a = 12 ⇒ a = 2
Q15. Simplify 5x - 2 + 3x + 7 - 4x + 1
View Answer
4x + 6
✅ SSC GD Exam Strategy
🟢 Practice combining like terms quickly and accurately
🟢 Master distributive property for multiplication
🟢 Learn to identify linear vs non-linear expressions
🟢 Practice mental calculations for basic operations
🟢 Time yourself - aim for 15-25 seconds per simplification
You've completed Linear Expressions!
SSC GD Tip: Mastering linear expressions is fundamental for algebra problems. Remember that linear expressions have degree 1 and can be simplified by combining like terms. Practice the four basic operations: addition, subtraction, multiplication by constants, and simplification. Regular practice with previous year SSC GD questions will build your speed and accuracy. Pay special attention to problems involving simplification and basic operations as they frequently appear in the exam.
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