Solve: `6x+5=2x+17`. Check the result.

Answer

To solve the equation \(6x + 5 = 2x + 17\), we will follow these steps:

### Step 1: Write down the equation
We start with the equation:
\[ 6x + 5 = 2x + 17 \]

### Step 2: Move all terms involving \(x\) to one side
To do this, we can subtract \(2x\) from both sides:
\[ 6x - 2x + 5 = 17 \]
This simplifies to:
\[ 4x + 5 = 17 \]

### Step 3: Move the constant term to the other side
Next, we subtract \(5\) from both sides:
\[ 4x + 5 - 5 = 17 - 5 \]
This simplifies to:
\[ 4x = 12 \]

### Step 4: Solve for \(x\)
Now, we divide both sides by \(4\):
\[ x = \frac{12}{4} \]
This gives us:
\[ x = 3 \]

### Step 5: Check the result
To verify our solution, we will substitute \(x = 3\) back into the original equation:
Left-hand side:
\[ 6(3) + 5 = 18 + 5 = 23 \]
Right-hand side:
\[ 2(3) + 17 = 6 + 17 = 23 \]

Since both sides are equal:
\[ 23 = 23 \]
Thus, the solution is correct.

### Final Answer:
The value of \(x\) is \(3\).

---