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Question

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

−5(3x−9)


(2 points)
Responses

5×3x+9
5 times 3 x plus 9

−15x+45
negative 15 x plus 45

15x−9
15 x minus 9

−15x−45
negative 15 x minus 45

−15x−9
negative 15 x minus 9

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

−5×3x−5×9
negative 5 times 3 x minus 5 times 9
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Answer 1

To determine which expressions are equivalent to \(-5(3x - 9)\), we can start by distributing the \(-5\) into the parenthesis:

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

Calculating each term:

1. \(-5 \cdot 3x = -15x\)
2. \(-5 \cdot (-9) = +45\)

Putting it all together, we get:

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

Now we can check the options provided:

1. 5×3x + 9 → Not equivalent.
2. −15x + 45 → This is equivalent.
3. 15x − 9 → Not equivalent.
4. −15x − 45 → Not equivalent.
5. −15x − 9 → Not equivalent.
6. −5×3x + −5×(−9) → This simplifies to \(-15x + 45\), which is equivalent.
7. −5×3x − 5×9 → This simplifies to \(-15x - 45\), which is not equivalent.

The two expressions that are equivalent to \(-5(3x - 9)\) are:

• −15x + 45
• −5×3x + −5×(−9)

So the correct responses are:

• −15x + 45
• −5×3x + −5×(−9)