Question

Which expression is equivalent to
2.5(x−1)+4.5(−x−2)?

Answer 1

To simplify the expression \( 2.5(x - 1) + 4.5(-x - 2) \), we will first distribute the constants in front of the parentheses.

1. Distributing \( 2.5 \) in the first term:
\[
2.5(x - 1) = 2.5x - 2.5
\]

2. Distributing \( 4.5 \) in the second term:
\[
4.5(-x - 2) = 4.5 \cdot (-x) + 4.5 \cdot (-2) = -4.5x - 9
\]

Now we can combine these results:
\[
2.5x - 2.5 - 4.5x - 9
\]

3. Combine like terms (the \( x \) terms and the constant terms):
- For the \( x \) terms:
\[
2.5x - 4.5x = -2x
\]
- For the constant terms:
\[
-2.5 - 9 = -11.5
\]

Putting it all together, we have:
\[
-2x - 11.5
\]

Thus, the expression \( 2.5(x - 1) + 4.5(-x - 2) \) is equivalent to:
\[
\boxed{-2x - 11.5}
\]