Question

Which expressions are equivalent to Negative 2 (5 x minus three-fourths)? Check all that apply.
Negative 2 (5 x) + (negative 2) (negative three-fourths)
Negative 10 x minus three-fourths
Negative 10 x + StartFraction 6 over 2 EndFraction
Negative 10 x + three-halves
Negative 10 x minus StartFraction 6 over 2 EndFraction

Answer 1

To find the expressions that are equivalent to \(-2(5x - \frac{3}{4})\), we first need to distribute \(-2\) across the terms inside the parentheses:

\[
-2(5x - \frac{3}{4}) = -2 \cdot 5x - 2 \cdot (-\frac{3}{4}) = -10x + \frac{3}{2}
\]

Now, let’s check which of the given expressions match this result.

1. **\(-2(5x) + (-2)(-\frac{3}{4})\)**
- This can be simplified as follows:
\[
-2(5x) + (-2)(-\frac{3}{4}) = -10x + \frac{3}{2}
\]
- **Equivalent!**

2. **\(-10x - \frac{3}{4}\)**
- This does not match.
- **Not equivalent!**

3. **\(-10x + \frac{6}{2}\)**
- Simplifying \(\frac{6}{2}\) gives:
\[
-10x + 3
\]
- This does not match.
- **Not equivalent!**

4. **\(-10x + \frac{3}{2}\)**
- This matches our result.
- **Equivalent!**

5. **\(-10x - \frac{6}{2}\)**
- Simplifying \(-\frac{6}{2}\) gives:
\[
-10x - 3
\]
- This does not match.
- **Not equivalent!**

Thus, the equivalent expressions are:

- \(-2 (5 x) + (-2)(-\frac{3}{4})\)
- \(-10x + \frac{3}{2}\)