To solve the inequality \( \frac{2}{5}m - 7 \leq 17 \), we'll follow these steps:
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Isolate the term with \(m\): Start by adding \(7\) to both sides of the inequality to eliminate the constant on the left side. \[ \frac{2}{5}m - 7 + 7 \leq 17 + 7 \] \[ \frac{2}{5}m \leq 24 \]
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Eliminate the fraction: To eliminate the fraction, multiply both sides by \(5\). Since \(5\) is a positive number, the direction of the inequality will not change. \[ 5 \cdot \frac{2}{5}m \leq 24 \cdot 5 \] \[ 2m \leq 120 \]
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Solve for \(m\): Finally, divide both sides by \(2\). Again, since \(2\) is positive, the direction of the inequality remains unchanged. \[ m \leq \frac{120}{2} \] \[ m \leq 60 \]
The solution to the inequality \( \frac{2}{5}m - 7 \leq 17 \) is: \[ m \leq 60 \]
Summary
- The inequality \( \frac{2}{5}m - 7 \leq 17 \) simplifies to \( m \leq 60 \).
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