Question

expressions that are equivalent to this algebraic expression

(2x - 1) - 3.25 (x + 3)

Answer 1

To simplify the expression \((2x - 1) - 3.25(x + 3)\), we can follow these steps:

1. Distribute \(-3.25\) to each term inside the parentheses:
\[
-3.25(x + 3) = -3.25x - 3.25 \cdot 3
\]
\[
= -3.25x - 9.75
\]

2. Now, substitute this back into the expression:
\[
(2x - 1) - (3.25x + 9.75)
\]

3. Combine like terms:
\[
= 2x - 1 - 3.25x - 9.75
\]
\[
= (2x - 3.25x) + (-1 - 9.75)
\]
\[
= -1.25x - 10.75
\]

The equivalent expression for \((2x - 1) - 3.25(x + 3)\) is:
\[
-1.25x - 10.75
\]

Other equivalent forms can be derived from this result, such as:
- Factored forms, e.g., \(-1.25(x + 8.6)\) (if we factor out \(-1.25\)).
- Expressing it in decimal or fraction form, as \(-\frac{5}{4}x - \frac{43}{4}\).

Thus, the simplified equivalent expression is:
\[
-1.25x - 10.75
\] or in fraction form:
\[
-\frac{5}{4}x - \frac{43}{4}
\]