Solve the inequalities for real x : `1/2((3x)/5+4)geq1/3(x-6)`

Explanation

To solve the inequality \( \frac{1}{2} \left( \frac{3x}{5} + 4 \right) \geq \frac{1}{3}(x - 6) \), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply both sides of the inequality by 30, which is the least common multiple of the denominators (2, 3, and 5).

\[ 30 \cdot \frac{1}{2} \left( \frac{3x}{5} + 4 \right) \geq 30 \cdot \frac{1}{3}(x - 6) \]
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