Using the properties of inequality, justify both steps in solving the inequality: 3/5x+6≥36

To solve the inequality \( \frac{3}{5}x + 6 \geq 36 \), we will follow these steps, justifying each step using the properties of inequality.

1. **Subtract 6 from both sides**:
\[
\frac{3}{5}x + 6 - 6 \geq 36 - 6
\]
This simplifies to:
\[
\frac{3}{5}x \geq 30
\]
**Justification**: According to the properties of inequalities, subtracting the same number from both sides of an inequality does not change the direction of the inequality.

2. **Multiply both sides by \(\frac{5}{3}\)** (the reciprocal of \(\frac{3}{5}\)):
\[
\frac{5}{3} \cdot \frac{3}{5}x \geq 30 \cdot \frac{5}{3}
\]
This simplifies to:
\[
x \geq 50
\]
**Justification**: When we multiply both sides of an inequality by a positive number, the direction of the inequality remains the same.

### Solution
The solution to the inequality is:
\[
x \geq 50
\]