How much smaller is `15x - 18y + 19z` than `22x - 20y - 13 z + 26` ?

Answer

To find out how much smaller the expression \( 15x - 18y + 19z \) is than \( 22x - 20y - 13z + 26 \), we can follow these steps:

### Step 1: Write the expressions
We have two expressions:
1. \( A = 15x - 18y + 19z \)
2. \( B = 22x - 20y - 13z + 26 \)

### Step 2: Set up the subtraction
To find out how much smaller \( A \) is than \( B \), we need to subtract \( A \) from \( B \):
\[ B - A = (22x - 20y - 13z + 26) - (15x - 18y + 19z) \]

### Step 3: Distribute the negative sign
Now, we distribute the negative sign across the terms in \( A \):
\[ B - A = 22x - 20y - 13z + 26 - 15x + 18y - 19z \]

### Step 4: Combine like terms
Now, we will combine the like terms:
- For \( x \): \( 22x - 15x = 7x \)
- For \( y \): \( -20y + 18y = -2y \)
- For \( z \): \( -13z - 19z = -32z \)
- The constant term remains \( +26 \)

Putting it all together, we get:
\[ B - A = 7x - 2y - 32z + 26 \]

### Final Answer
Thus, \( 15x - 18y + 19z \) is \( 7x - 2y - 32z + 26 \) smaller than \( 22x - 20y - 13z + 26 \).

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