\( 7 x<12 \) y \( 5 x>16 \)

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To solve the inequalities \( 7x < 12 \) and \( 5x > 16 \), we will solve each inequality separately. 1. **Solving \( 7x < 12 \)**: \[ x < \frac{12}{7} \] This simplifies to: \[ x < \approx 1.714 \] 2. **Solving \( 5x > 16 \)**: \[ x > \frac{16}{5} \] This simplifies to: \[ x > 3.2 \] Now we have two inequalities: - \( x < \frac{12}{7} \) (approximately 1.714) - \( x > \frac{16}{5} \) (3.2) Since there is no overlap between \( x < 1.714 \) and \( x > 3.2 \), there are no values of \( x \) that satisfy both inequalities simultaneously. Thus, the solution set is empty.