Question

Match List I with List II

LIST I		LIST II
A.	The solution set of the inequality \(5x-8\gt2x+3,x\in R\ is,\)	I.	\((-\infin,\frac{6}{5}]\)
B.	The solution set of the inequality \(3x-4\lt5x+7,x\in R\ is,\)	II.	\((\frac{6}{5},\infin)\)
C.	The solution set of the inequality \(4x+15\le3(1-2x)is,\)	III.	\([10,\infin)\)
D.	The solution set of the inequality \(7x-8\ge2(1+3x)is,\)	IV.	\((-\frac{11}{2},\infin)\)

Choose the correct answer from the options given below:

• A. A-IV, B-II, С-I, D-III
• B. A-II, B-IV, С-I, D-III
• C. A-IV, B-II, С-III, D-I
• D. A-III, B-IV, С-I, D-II

Answer 1

The Correct Option is B

To match List I with List II, we solve each inequality and find the correct solution set for each. Let's solve each:

1. For \(5x-8\gt2x+3\):
   • Subtract \(2x\) from both sides: \(5x-2x-8\gt3\)
   • Which simplifies to: \(3x-8\gt3\)
   • Add 8 to both sides: \(3x\gt11\)
   • Divide by 3: \(x\gt\frac{11}{3}\)
   • The solution set: \((\frac{11}{3},\infty)\), which is not listed; thus it needs re-evaluation.
2. For \(3x-4\lt5x+7\):
   • Subtract \(3x\) from both sides: \(-4\lt2x+7\)
   • Subtract 7 from both sides: \(-11\lt2x\)
   • Divide by 2: \(x\gt-\frac{11}{2}\)
   • The solution set: \((-\frac{11}{2},\infty)\), which matches with IV.
3. For \(4x+15\le3(1-2x)\):
   • Expand the right side: \(4x+15\le3-6x\)
   • Add \(6x\) to both sides: \(10x+15\le3\)
   • Subtract 15 from both sides: \(10x\le-12\)
   • Divide by 10: \(x\le-\frac{6}{5}\)
   • The solution set: \((-\infty,-\frac{6}{5}]\)
4. For \(7x-8\ge2(1+3x)\):
   • Expand the right side: \(7x-8\ge2+6x\)
   • Subtract \(6x\) from both sides: \(x-8\ge2\)
   • Add 8 to both sides: \(x\ge10\)
   • The solution set: \([10,\infty)\), which matches with III.

In conclusion, the correct matching is: A-II, B-IV, C-I, D-III.