Question

Select the TWO expressions that are equivalent to this algebraic expression:

−5(3x−9)

(2 points)
Responses

−15x−9

−15x+45

−15x−45

15x−9

−5×3x−5×9

5×3x+9

−5×3x+−5×(−9)

Answer 1

To simplify the expression \(-5(3x - 9)\):

1. Distribute \(-5\) to both terms inside the parentheses:

\[
-5 \cdot 3x + -5 \cdot (-9) = -15x + 45
\]

So, \(-5(3x - 9)\) simplifies to \(-15x + 45\).

Now we will look for equivalent expressions:

1. **\(-5 \times 3x - 5 \times 9\)**:
- This expression simplifies to:
\[
-15x - 45
\]
(This is not equivalent to \(-15x + 45\)).

2. **\(-15x + 45\)**:
- This is exactly what we found during simplification.

3. **\(-15x - 9\)**:
- This is not equivalent to \(-15x + 45\) (since the constant term is different).

4. **\(15x - 9\)**:
- This is also not equivalent to \(-15x + 45\).

5. **\(5 \times 3x + 9\)**:
- This simplifies to:
\[
15x + 9
\]
(This is not equivalent to \(-15x + 45\)).

6. **\(-5 \times 3x + -5 \times (-9)\)**:
- This simplifies to:
\[
-15x + 45
\]
(This matches our simplified result).

Thus, the two expressions that are equivalent to \(-5(3x - 9)\) are:

- **\(-15x + 45\)**
- **\(-5 \times 3x + -5 \times (-9)\)**