Solve the following equations :
`3(b-4)=2(4-b)`

Options

A. `5`
B. `6`
C. `4`
D. `3`

Answer

To solve the equation \( 3(b-4) = 2(4-b) \), we will follow these steps:

### Step 1: Distribute on both sides
Distribute the numbers outside the parentheses on both sides of the equation.

\[ 3(b - 4) = 2(4 - b) \]

This gives us:

\[ 3b - 12 = 8 - 2b \]

### Step 2: Move all terms involving \( b \) to one side
Next, we want to get all the \( b \) terms on one side and the constant terms on the other side. We can do this by adding \( 2b \) to both sides and adding \( 12 \) to both sides.

\[ 3b + 2b = 8 + 12 \]

This simplifies to:

\[ 5b = 20 \]

### Step 3: Solve for \( b \)
Now, we will divide both sides by \( 5 \) to solve for \( b \).

\[ b = \frac{20}{5} \]

This gives us:

\[ b = 4 \]

### Final Answer
The solution to the equation \( 3(b-4) = 2(4-b) \) is:

\[ b = 4 \]

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