Solve the following system of inequalities: $\frac{2x+1}{7x-1} > 5$ and $\frac{x+7}{x-8} > 2$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(NONE) For the first inequality: $\frac{2x+1}{7x-1} > 5$
$\Rightarrow \frac{2x+1}{7x-1} - 5 > 0$
$\Rightarrow \frac{2x+1 - 35x + 5}{7x-1} > 0$
$\Rightarrow \frac{-33x + 6}{7x-1} > 0$
$\Rightarrow \frac{33x - 6}{7x-1} < 0$
$\Rightarrow \frac{x - 2/11}{x - 1/7} < 0$
Thus,$x \in (1/7, 2/11)$.
For the second inequality: $\frac{x+7}{x-8} > 2$
$\Rightarrow \frac{x+7}{x-8} - 2 > 0$
$\Rightarrow \frac{x+7 - 2x + 16}{x-8} > 0$
$\Rightarrow \frac{-x + 23}{x-8} > 0$
$\Rightarrow \frac{x - 23}{x-8} < 0$
Thus,$x \in (8, 23)$.
The intersection of the intervals $(1/7, 2/11)$ and $(8, 23)$ is empty.
Therefore,there is no solution for the given system of inequalities.

Explore More

Similar Questions

$A$ company manufactures cassettes. Its cost and revenue functions are $C(x) = 26000 + 30x$ and $R(x) = 43x$,respectively,where $x$ is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realize some profit?

Difficult
View Solution

The set of real values of $x$ for which the inequality $|x-1|+|x+1| < 4$ holds true is

If $\frac{x^{2}-1}{x^{2}+1} \geq 0,$ then $x \in$

Let $a$ $(a < 0, a \notin I)$ be a constant and $t$ be a parameter. Then the set of values of $t$ for which the function $f(x) = \left( \frac{|[t]+1|+a}{|[t]+1|+1-a} \right)x$ is a decreasing function of $x$ (where $[.]$ denotes the greatest integer function) is:

The $IQ$ of a person is given by the formula $IQ = \frac{MA}{CA} \times 100$,where $MA$ is mental age and $CA$ is chronological age. If $80 \leq IQ \leq 140$ for a group of $12$ years old children,find the range of their mental age.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo