Linear Inequalities and Linear Programming
88522
If \(\frac{2 x+3}{5}\lt \frac{4 x-1}{2}\), then \(x\) lies \(x\) in the interval
1 \(\left[0, \frac{11}{16}\right)\)
2 \(\left[\frac{11}{16}, \infty\right)\)
3 \(\left(0, \frac{11}{16}\right)\)
4 \(\left(-\infty, \frac{11}{16}\right)\)
5 \(\left(\frac{11}{16}, \infty\right)\)
Explanation:
(E) : We have,
\(\frac{2 x+3}{5}\lt \frac{4 x-1}{2}\)
\(\frac{4 x-1}{2}-\frac{2 x+3}{5}>0\)
\(\frac{20 x-5-(4 x+6)}{10}>0\)
\(\frac{16 x-11}{10}>0\)
\(16 x-11>0\)
\(x>\frac{11}{16}\)