Linear InequalitiesMCQMTP Nov 20Question 1147 of 146
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The sol. set of the eq. x+2>0\displaystyle x+2 > 0 and 2x−6>0\displaystyle 2x-6 > 0 is

Options

A(−2,∞)\displaystyle (-2, \infty)
B(3,∞)\displaystyle (3, \infty)
C(−∞,2)\displaystyle (- \infty, 2)
D(−∞,3)\displaystyle (- \infty, 3)
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Correct Answer

✅ Option b — (3,∞)\displaystyle (3, \infty)

All Options:

  • A(−2,∞)\displaystyle (-2, \infty)
  • B(3,∞)\displaystyle (3, \infty)
  • C(−∞,2)\displaystyle (- \infty, 2)
  • D(−∞,3)\displaystyle (- \infty, 3)

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Detailed Solution & Explanation

Let's solve the system of inequalities:

1) First inequality:
x+2>0  ⟹  x>−2x + 2 > 0 \implies x > -2
2) Second inequality:
2x−6>0  ⟹  2x>6  ⟹  x>32x - 6 > 0 \implies 2x > 6 \implies x > 3

To satisfy both inequalities simultaneously, we take the intersection of their solution sets:
Solution Set={x∈R∣x>−2}∩{x∈R∣x>3}={x∈R∣x>3}\text{Solution Set} = \{x \in \mathbb{R} \mid x > -2\} \cap \{x \in \mathbb{R} \mid x > 3\} = \{x \in \mathbb{R} \mid x > 3\}
In interval notation, this is:
(3,∞)(3, \infty)x∈(3,∞)x \in (3, \infty)

This matches Option B.

Hence, **Option B** is the correct answer.

About This Chapter: Linear Inequalities

Paper

Paper 3: Quantitative Aptitude

Weightage

1-3 Marks

Key Topics

Linear Inequalities in one & two variables

This chapter covers Linear Inequalities in one & two variables and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 1-3 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Concepts to Understand

Set

A well-defined collection of distinct objects (called elements or members). Sets are denoted by capital letters and elements are listed within curly braces. Key operations include Union (∪), Intersection (∩), and Complement.

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