Question

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

−5(3x−9)


(2 points)
Responses

−15x−45
negative 15 x minus 45

15x−9
15 x minus 9

−15x−9
negative 15 x minus 9

−5×3x+−5×(−9)
negative 5 times 3 x plus negative 5 times negative 9

−15x+45
negative 15 x plus 45

−5×3x−5×9
negative 5 times 3 x minus 5 times 9

5×3x+9
5 times 3 x plus 9

Answer 1

To find the expressions equivalent to \(-5(3x - 9)\), we start by distributing the \(-5\) inside the parentheses:

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

Calculating each term:

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

Combining these results gives:

\[
-15x + 45
\]

Now we can look for equivalent expressions among the options provided.

1. **−15x−45**: This is **not equivalent** because it results in a negative constant term.

2. **15x−9**: This is **not equivalent**, as neither the coefficient of \(x\) nor the constant term matches.

3. **−15x−9**: This is **not equivalent**, as again, the constant term is incorrect.

4. **−5×3x+−5×(−9)**: This expression matches the distribution we performed and simplifies to the same result: \(-15x + 45\). Hence, it is **equivalent**.

5. **−15x+45**: This matches exactly what we calculated, so it is also **equivalent**.

6. **−5×3x−5×9**: This would yield \(-15x - 45\), which is not equivalent.

7. **5×3x+9**: This is equivalent to \(15x + 9\), which is not equivalent to the original expression.

The two expressions that are equivalent are:

- **−5×3x+−5×(−9)**
- **−15x+45**