Question:
If
\[
\frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in
\]
If
\[
\frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in
\]
Show Hint
When solving inequalities with fractions, always find a common denominator to simplify the process.
Updated On: Apr 7, 2026
- \( (0, 24) \)
- \( (-24, 0) \)
- \( (-24, 24) \)
- \( (0, 12) \)
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The Correct Option is C
Solution and Explanation
We start by solving the inequality:
\[
\frac{x}{4} + \frac{x}{3} < 13
\]
To eliminate the fractions, we find the least common denominator (LCD), which is 12:
\[
\frac{3x}{12} + \frac{4x}{12} < 13
\]
Simplifying the equation:
\[
\frac{7x}{12} < 13
\]
Multiplying both sides by 12:
\[
7x < 156
\]
Dividing both sides by 7:
\[
x < 22.2857
\]
Thus, the solution is \( x \in (-24, 24) \).
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