`((2x - 1)) /(3) ge ((3x - 2)) /(4) - ((2-x ))/(5)`

Explanation

To solve the inequality \(\frac{2x - 1}{3} \geq \frac{3x - 2}{4} - \frac{2 - x}{5}\), we will follow a systematic approach.

### Step-by-Step Solution:

1. **Rewrite the Inequality**:
Start with the given inequality:
\[ \frac{2x - 1}{3} \geq \frac{3x - 2}{4} - \frac{2 - x}{5} \]

2. **Find a Common Denominator**:
The common denominator for the fractions on the right side is 20. Rewrite each term:
\[ \frac{2x - 1}{3} \geq \frac{5(3x - 2)}{20} - \frac{4(2 - x)}{20} \]
This simplifies to:
\[ \frac{2x - 1}{3} \geq \frac{15x - 10 - 8 + 4x}{20} \]
Combine like terms:
\[ \frac{2x - 1}{3} \geq \frac{19x - 18}{20} \]

3. **Cross Multiply**:
To eliminate the fractions, cross-multiply:
\[ 20(2x - 1) \geq 3(19x - 18) \]
This expands to:
\[ 40x - 20 \geq 57x - 54 \]

4. **Rearrange the Inequality**:
Move all terms involving \(x\) to one side and constant terms to the other:
\[ 40x - 57x \geq -54 + 20 \]
Simplifying gives:
\[ -17x \geq -34 \]

5. **Divide by -17**:
When dividing by a negative number, remember to reverse the inequality:
\[ x \leq 2 \]

6. **Write the Solution**:
The solution in interval notation is:
\[ x \in (-\infty, 2] \]