Question:
Let $x$ be a real number such that $\dfrac{x-3}{x-2} \geq 1$. Then the solution set of the inequality is:
Let $x$ be a real number such that $\dfrac{x-3}{x-2} \geq 1$. Then the solution set of the inequality is:
Show Hint
Always simplify rational inequalities before applying sign analysis.
Updated On: Apr 24, 2026
- $(-\infty,3)$
- $(-\infty,2)$
- $[0,\infty)$
- $(-9,\infty)$
- $(0,8)$
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Concept:
• Solve rational inequalities by bringing all terms to one side
Step 1: Simplify inequality
\[ \frac{x-3}{x-2} - 1 \geq 0 \] \[ \frac{x-3 - (x-2)}{x-2} \geq 0 = \frac{-1}{x-2} \geq 0 \]
Step 2: Solve inequality
\[ \frac{-1}{x-2} \geq 0 \Rightarrow x-2<0 \Rightarrow x<2 \]
Step 3: Check restriction
\[ x \neq 2 \] Final Conclusion:
\[ (-\infty,2) \]
• Solve rational inequalities by bringing all terms to one side
Step 1: Simplify inequality
\[ \frac{x-3}{x-2} - 1 \geq 0 \] \[ \frac{x-3 - (x-2)}{x-2} \geq 0 = \frac{-1}{x-2} \geq 0 \]
Step 2: Solve inequality
\[ \frac{-1}{x-2} \geq 0 \Rightarrow x-2<0 \Rightarrow x<2 \]
Step 3: Check restriction
\[ x \neq 2 \] Final Conclusion:
\[ (-\infty,2) \]
Was this answer helpful?
0
0
Top KEAM Mathematics Questions
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
- The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is
- The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is
- Let $\Delta= \begin{vmatrix}1&1&1\\ 1&-1-w^{2}&w^{2}\\ 1&w&w^{4}\end{vmatrix}$, where $w \neq 1$ is a complex number such that $w^3 = 1$. Then $\Delta$ equals
- Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?
View More Questions
Top KEAM linear inequalities Questions
- If $|z + 1| < |z - 1|$ , then $z$ lies
- If $|x - 3| < 2x + 9$ then $x$ lies in the interval
- If $\frac{|x-3|}{x-3}$ > 0 , then
- If $ x $ satisfies the in equations $ 2x-7<11 $, $ 3x+4
- The set of all real $ x $ satisfying the in equal $ \frac{3-|x|}{4-|x|}\ge 0 $
View More Questions
Top KEAM Questions
- i.$\quad$ They help in respiration ii.$\quad$ They help in cell wall formation iii.$\quad$ They help in DNA replication iv. $\quad$They increase surface area of plasma membrane Which of the following prokaryotic structures has all the above roles?
- A body oscillates with SHM according to the equation (in SI units), $x = 5 cos \left(2\pi t +\frac{\pi}{4}\right) .$ Its instantaneous displacement at $t = 1$ second is
- The pH of a solution obtained by mixing 60 mL of 0.1 M BaOH solution at 40m of 0.15m HCI solution is
Kepler's second law (law of areas) of planetary motion leads to law of conservation of
- If $\int e^{2x}f' \left(x\right)dx =g \left(x\right)$, then $ \int\left(e^{2x}f\left(x\right) + e^{2x} f' \left(x\right)\right)dx =$
View More Questions