Question 11 markMCQSection A

The real x for which 2(2x+3)−10<6(x−2)2(2x + 3) - 10 < 6(x - 2) is :

Algebra (Linear Inequalities)
Linear Inequalities

Options

(A)x>2x > 2
(B)x>3x > 3
(C)x>4x > 4
(D)x>−4x > -4

Official answer

The correct option is C) x>4x > 4.


Working:


  • Expand: 2(2x+3)−10<6(x−2)2(2x + 3) - 10 < 6(x - 2)
  • 4x+6−10<6x−124x + 6 - 10 < 6x - 12
  • 4x−4<6x−124x - 4 < 6x - 12
  • Collect terms: 12−4<6x−4x12 - 4 < 6x - 4x
  • 8<2x8 < 2x, so x>4x > 4.
Answer keywords:linear inequalitytranspositionx > 4one variablesolution setinequality directionpositive divisor

Marking scheme

  1. 1.1 mark: correct simplification to 8<2x8 < 2x and final answer x>4x > 4 (option C).

Hint

Expand both brackets, gather x-terms on one side; dividing by a positive number does not flip the inequality.

Quick oral answer

Expanding gives 8<2x8 < 2x, so x>4x > 4; the sign stays the same because we divide by the positive number 2.

Common mistakes

  1. 1.Flipping the inequality sign even though division is by a positive number (+2).
  2. 2.Arithmetic slip in 6−10=−46 - 10 = -4 (often wrongly taken as -3 or +4).
  3. 3.Failing to transpose 6x6x to the left, leaving a wrong constant-only inequality.

Analysis and explanation

This tests solving a linear inequality in one variable by transposing terms.


Concept:


  • Expand both sides, bring variable terms to one side and constants to the other.
  • Dividing by a positive number (here +2) keeps the inequality direction unchanged.

Why C is correct:


  • 4x+6−10<6x−124x + 6 - 10 < 6x - 12 simplifies to 8<2x8 < 2x, i.e. x>4x > 4.

Why the distractors are wrong:


  • A (x>2x > 2): arises from a sign slip while transposing the constants.
  • B (x>3x > 3): comes from mis-adding 6 - 10 as -3 instead of -4.
  • D (x>−4x > -4): results from forgetting to move 6x across, or a sign error on the RHS constant.

Interesting facts

Linear inequalities are the algebraic backbone of Linear Programming — the feasible region in every LPP is just the overlap of several such inequalities.

Unlike equations, inequalities have infinitely many solutions, expressed as an interval — here (4,∞)(4, \infty).

Question details

Q1 of 44 questions

Board
CBSE
Class
Class 12
Subject
Applied Mathematics
Year
2026
Section
Section A
Marks
1
Type
MCQ
Chapter
Algebra (Linear Inequalities)
Topic
Linear Inequalities
Bloom's level
apply
Syllabus topic
Unit 2: Algebra — Solution of Linear Inequalities in one variable
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

When do we reverse the inequality sign?

Only when multiplying or dividing both sides by a negative number. Here we divide by +2, so the sign stays as it is and we get x>4x > 4.

How is the answer written as a set?

The solution is all real numbers greater than 4, written as the interval (4,∞)(4, \infty) or {x∈R:x>4}\{x \in R : x > 4\}.