Solve `9x+5=4(x-2)+8`

Options

A. `-1`
B. `-2`
C. `1`
D. `2`

Answer

To solve the equation \( 9x + 5 = 4(x - 2) + 8 \), we will follow these steps:

### Step 1: Expand the right side of the equation
Start by distributing the \( 4 \) on the right side of the equation:
\[ 4(x - 2) = 4x - 8 \]
So, the equation becomes:
\[ 9x + 5 = 4x - 8 + 8 \]

### Step 2: Simplify the right side
Combine like terms on the right side:
\[ 4x - 8 + 8 = 4x + 0 = 4x \]
Now, the equation is:
\[ 9x + 5 = 4x \]

### Step 3: Move all terms involving \( x \) to one side
Subtract \( 4x \) from both sides:
\[ 9x - 4x + 5 = 4x - 4x \]
This simplifies to:
\[ 5x + 5 = 0 \]

### Step 4: Move the constant term to the other side
Subtract \( 5 \) from both sides:
\[ 5x = 0 - 5 \]
This gives:
\[ 5x = -5 \]

### Step 5: Solve for \( x \)
Divide both sides by \( 5 \):
\[ x = \frac{-5}{5} \]
Thus, we find:
\[ x = -1 \]

### Final Answer
The solution to the equation is:
\[ x = -1 \]

---