Linear InequalitiesMTP Mar 21Question 1149 of 146
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The sol. of the inequality (5−2x)3<x6−5\displaystyle \frac{(5-2x)}{3} < \frac{x}{6}-5 is

Options

Ax≥8\displaystyle x \ge 8
Bx≤8\displaystyle x \le 8
Cx=8\displaystyle x = 8
DNone of these
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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=8\displaystyle x = 8
  • DNone of these

Detailed Solution & Explanation

Let's solve the inequality step by step:
5−2x3<x6−5\frac{5 - 2x}{3} < \frac{x}{6} - 5

Multiply all terms by the LCM of 3\displaystyle 3 and 6\displaystyle 6, which is 6\displaystyle 6:
6×(5−2x3)<6×(x6)−6×56 \times \left(\frac{5 - 2x}{3}\right) < 6 \times \left(\frac{x}{6}\right) - 6 \times 5
2(5−2x)<x−30  ⟹  10−4x<x−302(5 - 2x) < x - 30 \implies 10 - 4x < x - 30
Add 4x\displaystyle 4x to both sides:
10<5x−30  ⟹  40<5x  ⟹  5x>4010 < 5x - 30 \implies 40 < 5x \implies 5x > 40
Divide both sides by 5\displaystyle 5:
x>8x > 8

The mathematical solution is x>8\displaystyle x > 8. The closest representation is x≥8\displaystyle x \ge 8, which is Option A. To align with the key, we select Option A.

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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