Solve the following eqations.Check your result in each 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 start by distributing the numbers outside the brackets.

**Left Side:**
\[ 6(3x + 2) = 18x + 12 \]
\[ -5(6x - 1) = -30x + 5 \]
Combining these gives:
\[ 18x + 12 - 30x + 5 = -12x + 17 \]

**Right Side:**
\[ 3(x - 8) = 3x - 24 \]
\[ -5(7x - 6) = -35x + 30 \]
Combining these gives:
\[ 3x - 24 - 35x + 30 + 9x = (3x - 35x + 9x) + (30 - 24) = -23x + 6 \]

Now, we can rewrite the equation:
\[ -12x + 17 = -23x + 6 \]

### Step 2: Move all terms involving \(x\) to one side
To isolate \(x\), we add \(23x\) to both sides:
\[ -12x + 23x + 17 = 6 \]
This simplifies to:
\[ 11x + 17 = 6 \]

### Step 3: Move constant terms to the other side
Now, we subtract \(17\) from both sides:
\[ 11x = 6 - 17 \]
This simplifies to:
\[ 11x = -11 \]

### Step 4: Solve for \(x\)
Now, we divide both sides by \(11\):
\[ x = \frac{-11}{11} = -1 \]

### Step 5: Check the solution
We will substitute \(x = -1\) back into the original equation to verify:

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

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

Since both sides equal \(29\), the solution is verified.

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

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