Linear Inequalities

To solve the problem of matching List I with List II, we'll assess which solution set corresponds to each inequality in List I.

A. The inequality is $-5x%20%3E%203$ . Solving for $x$ :

$-5x%20%3E%203%20%5C%5C%20x%20%3C%20-%5Cfrac%7B3%7D%7B5%7D$

The solution set is $x%20%5Cin%20(-%5Cinfty%2C-%5Cfrac%7B3%7D%7B5%7D)$ , corresponding to IV.
B. The inequality is $%5Cfrac%7B-7x%7D%7B4%7D%20%5Cleq%20-5$ . Solving for $x$ :

$%5Cfrac%7B-7x%7D%7B4%7D%20%5Cleq%20-5%20%5C%5C%20-7x%20%5Cleq%20-20%20%5C%5C%20x%20%5Cgeq%20%5Cfrac%7B20%7D%7B7%7D$

The solution set is $x%20%5Cin%20%5B%5Cfrac%7B20%7D%7B7%7D%2C%5Cinfty)$ , corresponding to I.
C. The inequality is $7x%20-%204%20%5Cgeq%200$ . Solving for $x$ :

$7x%20%5Cgeq%204%20%5C%5C%20x%20%5Cgeq%20%5Cfrac%7B4%7D%7B7%7D$

The solution set is $x%20%5Cin%20%5B%5Cfrac%7B4%7D%7B7%7D%2C%5Cinfty)$ , corresponding to II.
D. The inequality is $9x%20-%204%20%3C%204x%20%2B%203$ . Solving for $x$ :

$5x%20%3C%207%20%5C%5C%20x%20%3C%20%5Cfrac%7B7%7D%7B5%7D$

The solution set is $x%20%5Cin%20(-%5Cinfty%2C%5Cfrac%7B7%7D%7B5%7D)$ , corresponding to III.

Thus, the correct matches are:

The correct answer from the options provided is:

(A)-(IV), (B)-(I), (C)-(II), (D)-(III)

	LIST I		LIST II
A.	The solution set of the inequality $-5x%20%3E%203%2C%20x%5Cin%20R$ , is	I.	$%5B%5Cfrac%7B20%7D%7B7%7D%2C%E2%88%9E)$
B.	The solution set of the inequality is, $%5Cfrac%7B-7x%7D%7B4%7D%20%E2%89%A4%20-5%2C%20x%5Cin%20R$ is,	II.	$%5B%5Cfrac%7B4%7D%7B7%7D%2C%E2%88%9E)$
C.	The solution set of the inequality $7x-4%E2%89%A50%2C%20x%5Cin%20R$ is,	III.	$(-%E2%88%9E%2C%5Cfrac%7B7%7D%7B5%7D)$
D.	The solution set of the inequality $9x-4%20%3C%204x%2B3%2C%20x%5Cin%20R$ is,	IV.	$(-%E2%88%9E%2C-%5Cfrac%7B3%7D%7B5%7D)$

Chapter Questions
1 MCQs