Verify and state the property used in each of the following.
`(-7) times (19+4)=[(-7) times 19]+[(-7) times 4]`

Answer

To verify the equation \((-7) \times (19 + 4) = [(-7) \times 19] + [(-7) \times 4]\) and state the property used, we will follow these steps:

### Step 1: Calculate the Left-Hand Side (LHS)
We start with the left-hand side of the equation:
\[ (-7) \times (19 + 4) \]
First, we need to simplify \(19 + 4\):
\[ 19 + 4 = 23 \]
Now, substitute this back into the equation:
\[ (-7) \times 23 \]
Next, we perform the multiplication:
\[ (-7) \times 23 = -161 \]

### Step 2: Calculate the Right-Hand Side (RHS)
Now, we calculate the right-hand side of the equation:
\[ [(-7) \times 19] + [(-7) \times 4] \]
First, calculate \((-7) \times 19\):
\[ (-7) \times 19 = -133 \]
Next, calculate \((-7) \times 4\):
\[ (-7) \times 4 = -28 \]
Now, substitute these values back into the RHS:
\[ -133 + (-28) \]
This can be simplified to:
\[ -133 - 28 \]
Now, perform the addition:
\[ -133 - 28 = -161 \]

### Step 3: Compare LHS and RHS
Now we compare the results from both sides:
- LHS = -161
- RHS = -161

Since both sides are equal, we have verified the equation.

### Conclusion
The property used in this verification is the **Distributive Property**, which states that:
\[ A \times (B + C) = (A \times B) + (A \times C) \]
In this case, \(A = -7\), \(B = 19\), and \(C = 4\).