Question

Simplify: -4(2x + 5)
A. (-4 - 2x) + (-4 - 5)
B. (-4 + 2x) multiplied by (-4 + 5)
C. (-4 divided by 2x) + (-4 divided by 5)
D. (-4 multiplied by 2x) + (-4 multiplied by 5)

Answer 1

are you sure this is correct

Answer 2

To simplify the expression \(-4(2x + 5)\), we can distribute \(-4\) to both terms inside the parentheses:

\[
-4(2x + 5) = -4 \cdot 2x + (-4) \cdot 5 = -8x - 20
\]

Now, let's evaluate the options provided:

A. \((-4 - 2x) + (-4 - 5)\)
- This simplifies to \(-4 - 2x - 4 - 5 = -2x - 13\) (not equivalent).

B. \((-4 + 2x) \text{ multiplied by } (-4 + 5)\)
- This simplifies to \((-4 + 2x) \cdot 1\), which gives \(-4 + 2x\) (not equivalent).

C. \((-4 \text{ divided by } 2x) + (-4 \text{ divided by } 5)\)
- This simplifies to \(-\frac{4}{2x} - \frac{4}{5}\) (not equivalent).

D. \((-4 \text{ multiplied by } 2x) + (-4 \text{ multiplied by } 5)\)
- This simplifies to \(-8x - 20\), which is equivalent to the original expression.

Therefore, the correct answer is:
**D. \((-4 \text{ multiplied by } 2x) + (-4 \text{ multiplied by } 5)\)**.

Answer 3

Yes, let's go through the simplification again to ensure clarity.

The original expression is:

\[
-4(2x + 5)
\]

We need to distribute \(-4\) across both terms inside the parentheses:

1. Multiply \(-4\) by \(2x\):
\[
-4 \cdot 2x = -8x
\]

2. Multiply \(-4\) by \(5\):
\[
-4 \cdot 5 = -20
\]

Now combine these results:

\[
-8x - 20
\]

So, the simplified expression is indeed \(-8x - 20\).

Now, let's evaluate the options again:

- **A.** \((-4 - 2x) + (-4 - 5)\) simplifies to:
\[
-4 - 2x - 4 - 5 = -2x - 13 \quad (\text{not equivalent})
\]

- **B.** \((-4 + 2x) \times (-4 + 5)\) simplifies to:
\[
(-4 + 2x) \times 1 = -4 + 2x \quad (\text{not equivalent})
\]

- **C.** \((-4 \div 2x) + (-4 \div 5)\) simplifies to:
\[
-\frac{4}{2x} - \frac{4}{5} \quad (\text{not equivalent})
\]

- **D.** \((-4 \times 2x) + (-4 \times 5)\) simplifies to:
\[
-8x - 20 \quad (\text{this is equivalent to } -8x - 20)
\]

Therefore, the correct choice is indeed **D.** \((-4 \text{ multiplied by } 2x) + (-4 \text{ multiplied by } 5)\), confirming that my previous analysis was accurate.