Solve the following equations and verify the results.
`6x+9=3x+57`

Answer

To solve the equation \(6x + 9 = 3x + 57\) and verify the results, we can follow these steps:

### Step 1: Write down the equation
We start with the equation:
\[ 6x + 9 = 3x + 57 \]

### Step 2: Move the terms involving \(x\) to one side
Subtract \(3x\) from both sides:
\[ 6x - 3x + 9 = 57 \]
This simplifies to:
\[ 3x + 9 = 57 \]

### Step 3: Move the constant term to the other side
Now, subtract \(9\) from both sides:
\[ 3x = 57 - 9 \]
This simplifies to:
\[ 3x = 48 \]

### Step 4: Solve for \(x\)
Now, divide both sides by \(3\):
\[ x = \frac{48}{3} \]
This simplifies to:
\[ x = 16 \]

### Step 5: Verification
To verify, we will substitute \(x = 16\) back into the original equation.

**Left Hand Side (LHS):**
\[ 6x + 9 = 6(16) + 9 = 96 + 9 = 105 \]

**Right Hand Side (RHS):**
\[ 3x + 57 = 3(16) + 57 = 48 + 57 = 105 \]

Since LHS = RHS, we have:
\[ 105 = 105 \]
Thus, the solution is verified.

### Final Answer
The solution to the equation \(6x + 9 = 3x + 57\) is:
\[ x = 16 \]