Download App

Linear Inequalities — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLinear Inequalities2 Marks
Question
Solve the inequality $\frac{3(x-2)}{5} \leq \frac{5(2-x)}{3}$ for real x.
✓

Answer

Here $\frac{{3(x - 2)}}{5} \leqslant \frac{{5(2 - x)}}{3}$
$ \Rightarrow \frac{{3x - 6}}{5} \leqslant \frac{{10 - 5x}}{3}$
$ \Rightarrow \frac{{3x}}{5} - \frac{6}{5} \leqslant \frac{{10}}{3} - \frac{{5x}}{3}$
$ \Rightarrow \frac{{3x}}{5} + \frac{{5x}}{3} \leqslant \frac{{10}}{3} + \frac{6}{5}$
$ \Rightarrow \frac{{9x + 25x}}{{15}} \leqslant \frac{{50 + 18}}{{15}}$
$ \Rightarrow \frac{{34x}}{{15}} \leqslant \frac{{68}}{{15}}$
Multiplying both sides by 15, we have
$34x \leqslant 68$
Dividing both sides by 34, we have
$x \leqslant 2$
Thus the solution set is $\left( { - \infty ,2} \right]$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Linear Inequalities→Linear Inequalities — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

How many terms are there in the A.P. whose first and fifth terms are -14 and 2 repectively and the sum of the terms is 40?
→
Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow\frac{-\pi}{2^+}}\sec\text{x}$
→
Find the domain and range of the function $f(x)=1-|x-2|$
→
Differentiate the following functions with respect to x:

$\frac{\text{x}\tan\text{x}}{\sec\text{x}+\tan\text{x}}$

→
Write the following relations as sets of ordered pairs and find which of them are functions:
$\{(\text{x},\text{y}):\text{y}=3\text{x},\text{x}\in\{1,2,3\},\text{y}\in\{3,6,9,12\}\}$
→
A die is thrown twice Each time the number appearing on it is recorded Describe the following events:
A = Both numbers are odd.
→
Write down all possible subsets of A = (1, {2, 3}).
→
Using the method of slope, show that the following points are collinear:
A(4, 8), B(5, 12), C(9, 28)
→
Find the value of $n$ such that :
(i) ${ }^n P _5=42{ }^n P _3, n>4$
(ii) $\frac{{ }^n P _4}{{ }^{n-1} P _4}=\frac{5}{3}, n>4$
→
Evaluate the following limits:
$\lim\limits_{\text{x}\rightarrow\infty}\frac{\text{x}}{\sqrt{4\text{x}^2+1}-1}$
→