Solve the following linear inequations in R: 3 x-2 <1 - Vidyadip

Question

Solve the following linear inequations in R: $\frac{3}{\text{x}-2}<1$

✓

Answer

$\frac{3}{\text{x}-2}<1$ $\frac{3}{\text{x}-2}-1<0$ $\frac{3-(\text{x}-2)}{\text{x}-2}<0$ $\frac{3-\text{x}+2}{\text{x}-2}<0$ $\frac{5-\text{x}}{\text{x}-2}<0$ $\frac{\text{x}-5}{\text{x}-2}>0$ Case1: x - 5 > 0 and x - 2 > 0 ⇒ x > 5 and x > 2 ⇒ x > 5 Case 2: x - 5 < 0 and x - 2 < 0 ⇒ x < 5 and x < 2 ⇒ x < 2 $\therefore$ solution set is $(-\infty,2)\cup(5,\infty)$

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 "(Each question 3 marks)" from Linear Inequations→Linear Inequations — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If A = {1, 2, 4} and B = {1, 2, 3}, represent following sets graphically:
A × A

It is required, to seat 5 men, and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?

Differentiate the following from first principle:$\text{e}^{\text{3x}}$

If $\sin\text{x}=\frac{3}{5},\tan\text{y}=\frac{1}{2}$ and $\frac{\pi}{2}<\text{x}<\pi<\text{y}<\frac{3\pi}{2},$ find the value of $8\tan\text{x}-\sqrt{5}\sec\text{y}.$

Find the values of $\theta$ and p, if the equation $\text{x} \cos θ + \text{y} \sin \theta = \text{p}$ is the normal form of the line $\sqrt{3}\text{x}+\text{y}+2=0.$

Show that for any sets A and B,

$\text{A}=(\text{A}\cap\text{B})\cap(\text{A - B})$

If $\tan\text{A}=\text{x}\tan\text{B},$ prove that $\frac{\sin\text{(A}-\text{B)}}{\sin\text{(A}+\text{B)}}=\frac{\text{x}-\text{1}}{\text{x}+\text{1}}$

If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
$(\text{A}\times\text{B})\cup(\text{A}\cup\text{C})$

If $S_1$ be the sum of ($2n + 1$) terms of an A.P. and $S_2$ be the sum of its odd terms, the prove that: $S_1 : S_2 = (2n + 1) : (n + 1)$

Prove that: $\Big\{1+\cot\text{x}-\sec\Big(\frac{\pi}{2}+\text{x}\Big)\Big\}\Big\{1+\cot\text{x}+\sec\Big(\frac{\pi}{2}+\text{x}\Big)\Big\}=2\cot\text{x}$