Question:
The least integer satisfying \( \frac{396}{10} - \frac{19-x}{10}<\frac{376}{10} - \frac{19-9x}{10} \) is:
The least integer satisfying \( \frac{396}{10} - \frac{19-x}{10}<\frac{376}{10} - \frac{19-9x}{10} \) is:
Show Hint
Be extremely careful with the negative signs before parentheses. A common mistake is forgetting to distribute the minus sign to both terms inside, e.g., $-(19-x) = -19+x$.
Updated On: May 2, 2026
- $1$
- $2$
- $3$
- $4$
- $5$
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
To solve a linear inequality involving fractions with a common denominator, we can multiply the entire inequality by that denominator to simplify the expression.
• If $a < b$, then $ka < kb$ for any positive $k$.
• After clearing denominators, group like terms and solve for $x$.
Step 1: Eliminate the denominators.
Multiply the entire inequality by $10$: \[ 396 - (19 - x) < 376 - (19 - 9x) \]
Step 2: Simplify both sides.
\[ 396 - 19 + x < 376 - 19 + 9x \] \[ 377 + x < 357 + 9x \]
Step 3: Solve for $x$.
Subtract $x$ and $357$ from both sides: \[ 377 - 357 < 9x - x \] \[ 20 < 8x \] \[ x > \frac{20}{8} \Rightarrow x > 2.5 \]
Step 4: Find the least integer.
The integers satisfying $x > 2.5$ are $\{3, 4, 5, \dots\}$. The least integer is $3$.
• If $a < b$, then $ka < kb$ for any positive $k$.
• After clearing denominators, group like terms and solve for $x$.
Step 1: Eliminate the denominators.
Multiply the entire inequality by $10$: \[ 396 - (19 - x) < 376 - (19 - 9x) \]
Step 2: Simplify both sides.
\[ 396 - 19 + x < 376 - 19 + 9x \] \[ 377 + x < 357 + 9x \]
Step 3: Solve for $x$.
Subtract $x$ and $357$ from both sides: \[ 377 - 357 < 9x - x \] \[ 20 < 8x \] \[ x > \frac{20}{8} \Rightarrow x > 2.5 \]
Step 4: Find the least integer.
The integers satisfying $x > 2.5$ are $\{3, 4, 5, \dots\}$. The least integer is $3$.
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