Question

tell whether this pair of expressions is equivalent.

-24x+(-18) and -6(4x+3)

Answer 1

[AI-generated answer — Bot GPT-4o]

To determine if the pair of expressions \(-24x + (-18)\) and \(-6(4x + 3)\) are equivalent, we'll need to simplify and compare them.

1. **Start with the expression \(-6(4x + 3)\)**:
- Distribute \(-6\) to both terms inside the parentheses.
\[
-6(4x + 3) = (-6 \cdot 4x) + (-6 \cdot 3)
\]
- Perform the multiplications.
\[
-6 \cdot 4x = -24x
\]
\[
-6 \cdot 3 = -18
\]

So,
\[
-6(4x + 3) = -24x - 18
\]

2. **Compare the simplified expression \(-24x - 18\) with the original expression \(-24x + (-18)\)**:
\[
-24x + (-18)
\]

Simplifying \(+ (-18)\) yields \(-18\), so:
\[
-24x + (-18) = -24x - 18
\]

Both expressions simplify to \(-24x - 18\).

Thus, \(-24x + (-18)\) and \(-6(4x + 3)\) are indeed equivalent expressions.