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.
-
\(-2(5x) + (-2)(-\frac{3}{4})\)
- This can be simplified as follows: \[ -2(5x) + (-2)(-\frac{3}{4}) = -10x + \frac{3}{2} \]
- Equivalent!
-
\(-10x - \frac{3}{4}\)
- This does not match.
- Not equivalent!
-
\(-10x + \frac{6}{2}\)
- Simplifying \(\frac{6}{2}\) gives: \[ -10x + 3 \]
- This does not match.
- Not equivalent!
-
\(-10x + \frac{3}{2}\)
- This matches our result.
- Equivalent!
-
\(-10x - \frac{6}{2}\)
- Simplifying \(-\frac{6}{2}\) gives: \[ -10x - 3 \]
- This does not match.
- Not equivalent!
Thus, the equivalent expressions are:
- \(-2 (5 x) + (-2)(-\frac{3}{4})\)
- \(-10x + \frac{3}{2}\)