To solve the inequality $\frac{2}{5}m-7\leq17$ using the properties of inequality, we need to justify both steps.
Step 1: Add 7 to both sides
By the addition property of inequality, we can add the same value to both sides of an inequality without changing the inequality. Therefore, we have:
$$\frac{2}{5}m-7+7 \leq 17 + 7$$
Simplifying, we get:
$$\frac{2}{5}m \leq 24$$
Step 2: Multiply both sides by $\frac{5}{2}$
To solve for $m$, we need to isolate the variable. Since $\frac{2}{5}$ is multiplied to $m$, we can undo this multiplication by multiplying both sides by the reciprocal, which is $\frac{5}{2}$. According to the multiplication property of inequality, we can multiply both sides of an inequality by a positive number without changing the inequality. Therefore, we have:
$$\frac{2}{5}m \times \frac{5}{2} \leq 24 \times \frac{5}{2}$$
Simplifying, we get:
$$m \leq 60$$
By justifying both steps using the properties of inequality, we have solved the inequality $\frac{2}{5}m-7\leq17$ and obtained the solution $m \leq 60$.
Using the properties of inequality, justify both steps in solving the inequality 2/5m−7≤17 .
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