Given, 5(x+4) – 8(4-x) = 25 - 3(7- x) + 144, then the value of x is

Options

A. 8
B. 16
C. 4
D. 11

Answer

To solve the equation \( 5(x + 4) - 8(4 - x) = 25 - 3(7 - x) + 144 \), we will follow these steps:

### Step 1: Expand the left side of the equation
We start by distributing the terms in the brackets.

\[ 5(x + 4) - 8(4 - x) = 5x + 20 - 32 + 8x \]

### Step 2: Combine like terms on the left side
Now we will combine the like terms on the left side.

\[ 5x + 20 - 32 + 8x = (5x + 8x) + (20 - 32) = 13x - 12 \]

### Step 3: Expand the right side of the equation
Next, we will expand the right side of the equation.

\[ 25 - 3(7 - x) + 144 = 25 - 21 + 3x + 144 \]

### Step 4: Combine like terms on the right side
Now we will combine the like terms on the right side.

\[ 25 - 21 + 144 + 3x = (25 - 21 + 144) + 3x = 148 + 3x \]

### Step 5: Set the left side equal to the right side
Now we have:

\[ 13x - 12 = 148 + 3x \]

### Step 6: Move all terms involving \( x \) to one side
Subtract \( 3x \) from both sides:

\[ 13x - 3x - 12 = 148 \]

This simplifies to:

\[ 10x - 12 = 148 \]

### Step 7: Move the constant to the other side
Add 12 to both sides:

\[ 10x = 148 + 12 \]

This simplifies to:

\[ 10x = 160 \]

### Step 8: Solve for \( x \)
Now, divide both sides by 10:

\[ x = \frac{160}{10} = 16 \]

### Final Answer
The value of \( x \) is \( 16 \).

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