Solve the following equations :
`6(6x-5)-5(7x-8)=12(4-x)+1`

Answer

To solve the equation \( 6(6x-5) - 5(7x-8) = 12(4-x) + 1 \), we will follow these steps:

### Step 1: Distribute the terms
We start by distributing the numbers outside the parentheses:

\[ 6(6x) - 6(5) - 5(7x) + 5(8) = 12(4) - 12(x) + 1 \]

This simplifies to:

\[ 36x - 30 - 35x + 40 = 48 - 12x + 1 \]

### Step 2: Combine like terms
Now, we combine the like terms on both sides of the equation:

On the left side:

\[ (36x - 35x) + (-30 + 40) = 1x + 10 \]

On the right side:

\[ 48 + 1 - 12x = 49 - 12x \]

So we have:

\[ x + 10 = 49 - 12x \]

### Step 3: Move all terms involving \( x \) to one side
Next, we will move all terms involving \( x \) to one side and the constant terms to the other side. We can do this by adding \( 12x \) to both sides:

\[ x + 12x + 10 = 49 \]

This simplifies to:

\[ 13x + 10 = 49 \]

### Step 4: Isolate \( x \)
Now, we will isolate \( x \) by subtracting 10 from both sides:

\[ 13x = 49 - 10 \]

This simplifies to:

\[ 13x = 39 \]

### Step 5: Solve for \( x \)
Finally, we divide both sides by 13 to solve for \( x \):

\[ x = \frac{39}{13} \]

This simplifies to:

\[ x = 3 \]

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

\[ x = 3 \]

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