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

Options

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

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 of the equation.

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

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 will combine like terms on the left side of the equation.

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

This simplifies to:
\[ 18x + 36 = 25x - 20 \]

### Step 3: Move all terms involving \( x \) to one side
Next, we will move all the \( x \) terms to one side and the constant terms to the other side.

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 of the equation.

\[ 36 + 20 = 7x \]

This gives us:
\[ 56 = 7x \]

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

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

Thus, the value of \( x \) that satisfies the equation is:
\[ \boxed{8} \]