Question:
Let $x$ be a real number such that $x+\frac{x}{4}+\frac{x}{3}<13$. Then the solution set is ________.
Let $x$ be a real number such that $x+\frac{x}{4}+\frac{x}{3}<13$. Then the solution set is ________.
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Clear fractions by multiplying the entire inequality by the LCM.
Updated On: Jun 26, 2026
- $(-\infty,\frac{156}{19})$
- $(\frac{156}{19},\infty)$
- $(\frac{154}{19},\infty)$
- $(-\infty,\frac{154}{17})$
- $(\frac{-156}{19},\frac{156}{19})$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
Combine like terms by finding a common denominator.
Step 2: Meaning
The LCM of 1, 4, and 3 is 12.
Step 3: Analysis
$\frac{12x + 3x + 4x}{12} < 13 \implies \frac{19x}{12} < 13 \implies 19x < 156$.
Step 4: Conclusion
$x < \frac{156}{19}$, which in interval notation is $(-\infty,\frac{156}{19})$. Final Answer: (A)
Combine like terms by finding a common denominator.
Step 2: Meaning
The LCM of 1, 4, and 3 is 12.
Step 3: Analysis
$\frac{12x + 3x + 4x}{12} < 13 \implies \frac{19x}{12} < 13 \implies 19x < 156$.
Step 4: Conclusion
$x < \frac{156}{19}$, which in interval notation is $(-\infty,\frac{156}{19})$. Final Answer: (A)
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