Linear Inequalities In One Variable

Step 1: Solve the inequality.
We are given the inequality:

%7C3x%20-%202%7C%20%5Cleq%20%5Cfrac%7B1%7D%7B2%7D.

This implies:

-%5Cfrac%7B1%7D%7B2%7D%20%5Cleq%203x%20-%202%20%5Cleq%20%5Cfrac%7B1%7D%7B2%7D.

Now, solve for

x

by adding 2 to all parts of the inequality:

%5Cfrac%7B3%7D%7B2%7D%20%5Cleq%203x%20%5Cleq%20%5Cfrac%7B5%7D%7B2%7D.

Next, divide by 3:

%5Cfrac%7B1%7D%7B2%7D%20%5Cleq%20x%20%5Cleq%20%5Cfrac%7B5%7D%7B6%7D.

Step 2: Conclusion.
Thus,

x

lies in the interval

%5Cleft%5B%20%5Cfrac%7B1%7D%7B2%7D%2C%20%5Cfrac%7B5%7D%7B6%7D%20%5Cright%5D

, which corresponds to option (A).

Chapter Questions
2 MCQs