Question

If \[ \frac{x}{4} + \frac{x}{3} < 13, \text{ then } x \in \]

• A. \( (0, 24) \)
• B. \( (-24, 0) \)
• C. \( (-24, 24) \)
• D. \( (0, 12) \)

Hint:

When solving inequalities with fractions, always find a common denominator to simplify the process.

Answer 1

The Correct Option is C

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 \( x \in (-24, 24) \).