Solve the equations and check your answer in the case:
`6(3x+2)-5(6x-1)=3(x-8)-5(7x-6)+9x`

Answer

To solve the equation \( 6(3x + 2) - 5(6x - 1) = 3(x - 8) - 5(7x - 6) + 9x \), we will follow these steps:

### Step 1: Expand both sides of the equation
We will distribute the coefficients across the terms inside the brackets.

**Left Hand Side (LHS):**
\[ 6(3x + 2) - 5(6x - 1) = 18x + 12 - 30x + 5 \]
Combine like terms:
\[ (18x - 30x) + (12 + 5) = -12x + 17 \]

**Right Hand Side (RHS):**
\[ 3(x - 8) - 5(7x - 6) + 9x = 3x - 24 - 35x + 30 + 9x \]
Combine like terms:
\[ (3x - 35x + 9x) + (-24 + 30) = -23x + 6 \]

Now, we have:
\[ -12x + 17 = -23x + 6 \]

### Step 2: Rearrange the equation
We will move all terms involving \( x \) to one side and constant terms to the other side.

Add \( 23x \) to both sides:
\[ -12x + 23x + 17 = 6 \]
This simplifies to:
\[ 11x + 17 = 6 \]

Next, subtract \( 17 \) from both sides:
\[ 11x = 6 - 17 \]
This simplifies to:
\[ 11x = -11 \]

### Step 3: Solve for \( x \)
Now, divide both sides by \( 11 \):
\[ x = \frac{-11}{11} = -1 \]

### Step 4: Check the solution
We will substitute \( x = -1 \) back into the original equation to verify.

**Left Hand Side:**
\[ 6(3(-1) + 2) - 5(6(-1) - 1) = 6(-3 + 2) - 5(-6 - 1) \]
This simplifies to:
\[ 6(-1) - 5(-7) = -6 + 35 = 29 \]

**Right Hand Side:**
\[ 3(-1 - 8) - 5(7(-1) - 6) + 9(-1) = 3(-9) - 5(-7 - 6) - 9 \]
This simplifies to:
\[ -27 - 5(-13) - 9 = -27 + 65 - 9 = 29 \]

Since both sides are equal:
\[ LHS = 29 \quad \text{and} \quad RHS = 29 \]
Thus, the solution is verified.

### Final Answer:
\[ x = -1 \]