To solve the inequality \( \frac{2}{5}m - 7 \leq 17 \), we can go through the steps one-by-one while justifying each operation using properties of inequalities.
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Add 7 to both sides:
The first step is to eliminate the constant on the left side. We do this by adding 7 to both sides of the inequality: \[ \frac{2}{5}m - 7 + 7 \leq 17 + 7 \] This simplifies to: \[ \frac{2}{5}m \leq 24 \] Justification: Adding the same number to both sides of an inequality does not change the direction of the inequality. -
Multiply both sides by \( \frac{5}{2} \):
The next step is to isolate \( m \) by multiplying both sides by \( \frac{5}{2} \): \[ m \leq 24 \times \frac{5}{2} \] This simplifies to: \[ m \leq 60 \] Justification: When multiplying or dividing both sides of an inequality by a positive number, the direction of the inequality remains unchanged.
Thus, after solving, we find that \( m \leq 60 \).
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