The value of x which satisfies the equation
`10 (x + 6) + 8 (x - 3) = 5 (5x - 4)` also stisfies the equation

Options

A. `5(x - 5) = 2(X - 3) + 5`
B. `5(x - 3) = x + 5`
C. `3 (3x - 5) = 2x + 1`
D. `2 (x + 3) = 5 (x - 5) + 4`

Answer

To solve the equation \(10(x + 6) + 8(x - 3) = 5(5x - 4)\), we will follow these steps:

### Step 1: Expand both sides of the equation
We start by distributing the terms on both sides:

\[ 10(x + 6) + 8(x - 3) = 5(5x - 4) \]

Expanding the left side:

\[ 10x + 60 + 8x - 24 \]

Expanding the right side:

\[ 25x - 20 \]

So, the equation becomes:

\[ 10x + 60 + 8x - 24 = 25x - 20 \]

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

\[ (10x + 8x) + (60 - 24) = 25x - 20 \]

This simplifies to:

\[ 18x + 36 = 25x - 20 \]

### Step 3: Move all terms involving \(x\) to one side
Next, we will move all terms involving \(x\) to one side and constant terms to the other side. We can subtract \(18x\) from both sides:

\[ 36 = 25x - 18x - 20 \]

This simplifies to:

\[ 36 = 7x - 20 \]

### Step 4: Isolate \(x\)
Now, we will isolate \(x\) by adding 20 to both sides:

\[ 36 + 20 = 7x \]

This gives us:

\[ 56 = 7x \]

### Step 5: Solve for \(x\)
Finally, we will divide both sides by 7 to solve for \(x\):

\[ x = \frac{56}{7} = 8 \]

### Conclusion
The value of \(x\) that satisfies the equation is:

\[ \boxed{8} \]