Equations And Inequalities Question 3
Question: If $ \frac{3x-4}{2}\ge \frac{x+1}{4}-1, $ then $ x\in $
Options:
A) $ [1,\infty ) $
B) $ (1,\infty ) $
C) $ (-5,5) $
D) $ [-5,5] $
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] We have $ \frac{3x-4}{2}\ge \frac{x+1}{4}-1 $ or $ \frac{3x-4}{2}\ge \frac{x-3}{4} $ or $ 2(3x-4)\ge (x-3),or6x-8\ge x-3 $ or $ 5x\ge 5 $ or $ x\ge 1 $ Thus, all real numbers which are greater than or equal to 1 is the solution set of the given inequality.
$ \therefore x\in [1,\infty ). $
BETA
