Solve : ` (5x - 2)/(3) lt (4x-7)/(2)`

Explanation

To solve the inequality \(\frac{5x - 2}{3} < \frac{4x - 7}{2}\), we will follow these steps:

### Step 1: Eliminate the fractions
To eliminate the fractions, we can multiply both sides of the inequality by the least common multiple (LCM) of the denominators, which is 6.

\[ 6 \cdot \frac{5x - 2}{3} < 6 \cdot \frac{4x - 7}{2} \]

### Step 2: Simplify both sides
Now, we simplify both sides:

\[ 2(5x - 2) < 3(4x - 7) \]

Expanding both sides gives:

\[ 10x - 4 < 12x - 21 \]

### Step 3: Rearrange the inequality
Next, we will rearrange the inequality to isolate the variable \(x\). We can move the \(x\) terms to one side and the constant terms to the other side:

\[ 10x - 12x < -21 + 4 \]

This simplifies to:

\[ -2x < -17 \]

### Step 4: Divide by -2
When we divide both sides by -2, we must reverse the inequality sign:

\[ x > \frac{17}{2} \]

### Final Answer
Thus, the solution to the inequality is:

\[ x > \frac{17}{2} \]