Which expressions are equivalent to Negative 2 (5 x minus three-fourths)? Check all that apply.

Question

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:

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