Solve: `3(x+6)+2(x+3)=64`. Check the result.

Answer

To solve the equation \(3(x + 6) + 2(x + 3) = 64\), we will follow these steps:

### Step 1: Distribute the terms
First, we will distribute the numbers outside the brackets to the terms inside the brackets.

\[ 3(x + 6) = 3x + 18 \]
\[ 2(x + 3) = 2x + 6 \]

So, the equation becomes:
\[ 3x + 18 + 2x + 6 = 64 \]

### Step 2: Combine like terms
Next, we will combine the like terms on the left side of the equation.

\[ 3x + 2x + 18 + 6 = 64 \]
\[ 5x + 24 = 64 \]

### Step 3: Isolate the variable
Now, we will isolate the variable \(x\) by moving the constant term to the right side of the equation.

\[ 5x = 64 - 24 \]
\[ 5x = 40 \]

### Step 4: Solve for \(x\)
Next, we will divide both sides by 5 to solve for \(x\).

\[ x = \frac{40}{5} \]
\[ x = 8 \]

### Step 5: Check the result
To verify our solution, we will substitute \(x = 8\) back into the original equation.

Original equation:
\[ 3(x + 6) + 2(x + 3) = 64 \]

Substituting \(x = 8\):
\[ 3(8 + 6) + 2(8 + 3) = 64 \]
\[ 3(14) + 2(11) = 64 \]
\[ 42 + 22 = 64 \]
\[ 64 = 64 \]

Since both sides of the equation are equal, our solution is verified.

### Final Answer:
\[ x = 8 \]

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