Solve : `(3)/(5)(4x-9) - (5)/(4)(3x-8) = 5-(7)/(10)(2x-1)`.

Answer

To solve the equation \(\frac{3}{5}(4x-9) - \frac{5}{4}(3x-8) = 5 - \frac{7}{10}(2x-1)\), we will follow these steps:

### Step 1: Eliminate the fractions by finding a common denominator.
The denominators in the equation are 5, 4, and 10. The least common multiple (LCM) of these denominators is 20. We will multiply each term by 20 to eliminate the fractions.

\[ 20 \left( \frac{3}{5}(4x-9) \right) - 20 \left( \frac{5}{4}(3x-8) \right) = 20 \left( 5 - \frac{7}{10}(2x-1) \right) \]

### Step 2: Distribute the 20.
Distributing 20 to each term gives us:

\[ 4 \cdot 3(4x-9) - 5 \cdot 5(3x-8) = 100 - 2 \cdot 7(2x-1) \]

This simplifies to:

\[ 12(4x-9) - 25(3x-8) = 100 - 14(2x-1) \]

### Step 3: Expand the expressions.
Now we expand both sides:

\[ 48x - 108 - 75x + 200 = 100 - 28x + 14 \]

### Step 4: Combine like terms.
On the left side, combine the \(x\) terms and the constant terms:

\[ (48x - 75x) + (200 - 108) = 100 + 14 - 28x \]

This simplifies to:

\[ -27x + 92 = 114 - 28x \]

### Step 5: Move all \(x\) terms to one side and constant terms to the other side.
Add \(28x\) to both sides and subtract \(92\) from both sides:

\[ -27x + 28x = 114 - 92 \]

This simplifies to:

\[ x = 22 \]

### Final Answer:
The solution to the equation is \(x = 22\).

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