Question:
Let $x$ be a real number such that $\frac{3(x+3)}{7} \le \frac{6(x-1)}{5}$. Then the solution set of the inequality is:
Let $x$ be a real number such that $\frac{3(x+3)}{7} \le \frac{6(x-1)}{5}$. Then the solution set of the inequality is:
Show Hint
Always simplify the fraction $\frac{87}{27}$ by dividing both numerator and denominator by 3.
Updated On: Apr 28, 2026
- $(-\infty, \frac{29}{9})$
- $(\frac{29}{9}, \infty)$
- $[\frac{29}{9}, \infty)$
- $(-\infty, \infty)$
- $(\frac{17}{9}, \infty)$
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Analysis
Cross-multiply to remove fractions: $5 \cdot 3(x+3) \le 7 \cdot 6(x-1)$. $15(x+3) \le 42(x-1)$.
Step 2: Calculation
$15x + 45 \le 42x - 42$. $45 + 42 \le 42x - 15x$. $87 \le 27x$.
Step 3: Calculation
$x \ge \frac{87}{27} = \frac{29}{9}$. Final Answer: (C)
Cross-multiply to remove fractions: $5 \cdot 3(x+3) \le 7 \cdot 6(x-1)$. $15(x+3) \le 42(x-1)$.
Step 2: Calculation
$15x + 45 \le 42x - 42$. $45 + 42 \le 42x - 15x$. $87 \le 27x$.
Step 3: Calculation
$x \ge \frac{87}{27} = \frac{29}{9}$. Final Answer: (C)
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 in one variable Questions
- The least integer satisfying $\frac{396}{10}-\frac{19-x}{10} < \frac{376}{10}-\frac{19-9x}{10}$ is
- Solution set of \( -12x > 38 \text{ for } x \in \mathbb{N} \) \[ -12x > 38 \]
- If \[ \frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in \]
- Number of words that can be formed starting and ending with the same letter from the word BANANA.
- The coefficient of \( x^3 \) in \( (2+x)^n \) is 160. Find the coefficient of \( x^6 \) in \( (2-x^2)^n \).
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