Stewart Kelley
09/04/2024 · Junior High School
\( 7 x<12 \) y \( 5 x>16 \)
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Tutor-Verified Answer
Step-by-step Solution
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:
\[
x < \frac{12}{7} \approx 1.714
\]
2. **Solving \( 5x > 16 \)**:
\[
x > \frac{16}{5}
\]
This simplifies to:
\[
x > \frac{16}{5} = 3.2
\]
Now we have two inequalities:
- \( x < \frac{12}{7} \) (approximately 1.714)
- \( x > 3.2 \)
Since there are no values of \( x \) that can satisfy both inequalities simultaneously (as \( x \) cannot be both less than 1.714 and greater than 3.2 at the same time), the solution set is empty.
Thus, there are no values of \( x \) that satisfy both inequalities.
Quick Answer
There are no values of \( x \) that satisfy both inequalities.
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