`((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 these steps:

### Step 1: Find a common denominator for the right side
The denominators are 4 and 5, so the least common multiple (LCM) is 20. We will rewrite each term on the right side with a denominator of 20.

\[ \frac{3x - 2}{4} = \frac{5(3x - 2)}{20} = \frac{15x - 10}{20} \]

\[ \frac{2 - x}{5} = \frac{4(2 - x)}{20} = \frac{8 - 4x}{20} \]

Now we can rewrite the inequality:

\[ \frac{2x - 1}{3} \geq \frac{15x - 10 - (8 - 4x)}{20} \]

### Step 2: Simplify the right side
Combine the terms in the numerator:

\[ 15x - 10 - 8 + 4x = 19x - 18 \]

So the inequality becomes:

\[ \frac{2x - 1}{3} \geq \frac{19x - 18}{20} \]

### Step 3: Cross-multiply
To eliminate the fractions, we cross-multiply:

\[ 20(2x - 1) \geq 3(19x - 18) \]

### Step 4: Distribute both sides
Distributing gives us:

\[ 40x - 20 \geq 57x - 54 \]

### Step 5: Rearrange the inequality
Now, we will move all terms involving \(x\) to one side and constant terms to the other side:

\[ 40x - 57x \geq -54 + 20 \]

This simplifies to:

\[ -17x \geq -34 \]

### Step 6: Divide by -17
When dividing by a negative number, we must reverse the inequality sign:

\[ x \leq 2 \]

### Final Solution
The solution to the inequality is:

\[ x \leq 2 \]

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