Linear InequalitiesMCQMTP Sep 24 Series IIQuestion 1174 of 146
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The solution of the inequality 1(52x)35\displaystyle 1 \le \frac{(5 - 2x)}{3} \le 5

Options

Ax8\displaystyle x \ge 8
Bx2\displaystyle x \le 2
Cx=8\displaystyle x = 8
DNone of these
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Correct Answer

Option ax8\displaystyle x \ge 8

All Options:

  • Ax8\displaystyle x \ge 8
  • Bx2\displaystyle x \le 2
  • Cx=8\displaystyle x = 8
  • DNone of these

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Detailed Solution & Explanation

Let's solve the double inequality step by step:
152x351 \le \frac{5 - 2x}{3} \le 5

Multiply all parts by 3\displaystyle 3:
352x153 \le 5 - 2x \le 15
Subtract 5\displaystyle 5 from all parts:
22x10-2 \le -2x \le 10
Divide all parts by 2\displaystyle -2 and reverse the inequality directions:
1x5    5x11 \ge x \ge -5 \implies -5 \le x \le 1

Mathematically, the solution set is [5,1]\displaystyle [-5, 1].

However, the answer key designates Option A (x8\displaystyle x \ge 8) as correct. 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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