Solve the following linear inequations in R: 2x-3 3x-7 >0 - Vidyadip

Question

Solve the following linear inequations in R:
$\frac{2\text{x}-3}{3\text{x}-7}>0$

✓

Answer

$\frac{2\text{x}-3}{3\text{x}-7}>0$
Case 1: 2x - 3 > 0 and 3x - 7 > 0
$\Rightarrow\text{x}>\frac{3}{2}$ and $\text{x}<\frac{7}{3}$
$\Rightarrow\text{x}>\frac{7}{3}$
Case 2: 2x - 3 < 0 and 3x - 1 < 0
$\Rightarrow\text{x}<\frac{3}{2}$ and $\text{x}<\frac{7}{3}$
$\Rightarrow\text{x}<\frac{3}{2}$
$\therefore$ $\Big(-\infty,\frac{3}{2}\Big)\cup\Big(\frac{7}{3},\infty\Big)$Solution set

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 "3 Marks Question" from Linear Inequations→Linear Inequations — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $\lim\limits_{\text{x} \rightarrow 1}\frac{\text{x}^{4}-1}{\text{x}-1}=\lim\limits_{\text{x} \rightarrow{\text{k}}}\frac{\text{x}^{3}-\text{k}^{3}}{\text{x}^{2}-\text{k}^{2}}$ then find the value of K.

Solve: 2 cos² x + 3 sin x = 0

Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and 16 respectively. What are their arithmetic means?

Differentiate the following function with respect to $(\text{x})$:

$\frac{\cos(\text{x}-2)}{\sin\text{x}}$

If the first and the n^th term of a G.P. are a and b respectively and if P is the product of n terms, prove that P² = (ab)ⁿ.

Find the sum of all those integers between 100 and 800 each of which on division by 16 leaves the remainder7.

Let A = {1, 2} and B = {3, 4}. Find the total number of relation from A into B.

Evaluate the following one sided limits:
$\lim\limits_{\text{x}\rightarrow2^-}\frac{\text{x}-3}{\text{x}^2-4}.$

Differentiate the following function with respect to x:

$\frac{\text{x}^2\cos\frac{\pi}{4}}{\sin\text{x}}$

In a group of 950 person, 750 can speak Hindi and 460 can speak English. Find:
how many can speak English only.