Solve: `((5x-3))/6-((2x-1))/3=((4-3x))/2`

Answer

To solve the equation \(\frac{5x - 3}{6} - \frac{2x - 1}{3} = \frac{4 - 3x}{2}\), we will follow these steps:

### Step 1: Find a common denominator
The denominators in the equation are 6, 3, and 2. The least common multiple (LCM) of these numbers is 6.

### Step 2: Rewrite the equation with the common denominator
We can rewrite each term with the common denominator of 6:
\[ \frac{5x - 3}{6} - \frac{2(2x - 1)}{6} = \frac{3(4 - 3x)}{6} \]
This simplifies to:
\[ \frac{5x - 3 - (4x - 2)}{6} = \frac{12 - 9x}{6} \]

### Step 3: Eliminate the denominator
Since both sides of the equation have the same denominator (6), we can multiply both sides by 6 to eliminate the denominator:
\[ 5x - 3 - (4x - 2) = 12 - 9x \]

### Step 4: Simplify the left side
Distributing the negative sign on the left side:
\[ 5x - 3 - 4x + 2 = 12 - 9x \]
Combining like terms:
\[ (5x - 4x) + (-3 + 2) = 12 - 9x \]
This simplifies to:
\[ x - 1 = 12 - 9x \]

### Step 5: Move all terms involving \(x\) to one side
Add \(9x\) to both sides:
\[ x + 9x - 1 = 12 \]
This simplifies to:
\[ 10x - 1 = 12 \]

### Step 6: Isolate \(x\)
Add 1 to both sides:
\[ 10x = 12 + 1 \]
This simplifies to:
\[ 10x = 13 \]

### Step 7: Solve for \(x\)
Divide both sides by 10:
\[ x = \frac{13}{10} \]

### Final Answer
Thus, the solution to the equation is:
\[ x = \frac{13}{10} \]

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