By how much is -12x + 2y greater than the sum of -18x + 6y and 5x - 25y ?

Options

A. x + 21y
B. `-x - 21y`
C. x + 25y
D. x + 36y

Answer

To solve the question "By how much is -12x + 2y greater than the sum of -18x + 6y and 5x - 25y?", we will follow these steps:

### Step 1: Calculate the sum of -18x + 6y and 5x - 25y.

We start by adding the two expressions:

\[ -18x + 6y + 5x - 25y \]

### Step 2: Combine like terms.

Now, we combine the x terms and the y terms separately:

\[ (-18x + 5x) + (6y - 25y) \]

Calculating the x terms:

\[ -18x + 5x = -13x \]

Calculating the y terms:

\[ 6y - 25y = -19y \]

So, the sum is:

\[ -13x - 19y \]

### Step 3: Now, we need to find out how much -12x + 2y is greater than this sum.

We set up the equation:

\[ -12x + 2y - (-13x - 19y) \]

### Step 4: Simplify the expression.

This simplifies to:

\[ -12x + 2y + 13x + 19y \]

### Step 5: Combine like terms again.

Now, we combine the x terms and the y terms:

\[ (-12x + 13x) + (2y + 19y) \]

Calculating the x terms:

\[ -12x + 13x = 1x \quad \text{or simply } x \]

Calculating the y terms:

\[ 2y + 19y = 21y \]

### Final Result:

Putting it all together, we have:

\[ x + 21y \]

Thus, -12x + 2y is greater than the sum of -18x + 6y and 5x - 25y by:

\[ x + 21y \]