Linear InequalitiesPYQ Jan 26Question 4501 of 73
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The solution of the inequality 5−2x3≤x6−5\displaystyle \frac{5-2x}{3} \le \frac{x}{6} - 5 is

Options

Ax≥8\displaystyle x \ge 8
Bx≤8\displaystyle x \le 8
Cx≥6\displaystyle x \ge 6
Dx≤6\displaystyle x \le 6
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Correct Answer

✅ Option a — x≥8\displaystyle x \ge 8

All Options:

  • Ax≥8\displaystyle x \ge 8
  • Bx≤8\displaystyle x \le 8
  • Cx≥6\displaystyle x \ge 6
  • Dx≤6\displaystyle x \le 6

Detailed Solution & Explanation

Given inequality:
5−2x3≤x6−5\frac{5-2x}{3} \le \frac{x}{6} - 5

To clear the fractions, multiply both sides of the inequality by the least common multiple of 3\displaystyle 3 and 6\displaystyle 6, which is 6\displaystyle 6:
6×(5−2x3)≤6×(x6−5)6 \times \left(\frac{5-2x}{3}\right) \le 6 \times \left(\frac{x}{6} - 5\right)2(5−2x)≤x−302(5 - 2x) \le x - 30
Expand the left side:
10−4x≤x−3010 - 4x \le x - 30

Add 4x\displaystyle 4x to both sides of the inequality:
10≤5x−3010 \le 5x - 30

Add 30\displaystyle 30 to both sides of the inequality:
40≤5x40 \le 5x

Divide both sides by 5\displaystyle 5 (since 5\displaystyle 5 is positive, the inequality sign remains the same):
8≤x  ⟹  x≥88 \le x \implies x \ge 8

Hence, **Option A** 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.

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