# Question Video: Recognizing Equivalent Expressions Mathematics • 7th Grade

Which of the following expressions is equivalent to −9(5 − 6𝑥)? [A] −45 + 54𝑥 [B] 45 − 54𝑥 [C] −45 − 54𝑥 [D] −45 + 6𝑥 [E] −45 − 6𝑥

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### Video Transcript

Which of the following expressions is equivalent to negative nine multiplied by five minus six 𝑥? Is it A) negative 45 plus 54𝑥, B) 45 minus 54𝑥, C) negative 45 minus 54𝑥, D) negative 45 plus six 𝑥, or E) negative 45 minus six 𝑥?

In order to answer this question, we need to distribute the parentheses. This is also called expanding the bracket. We need to multiply the term outside of the bracket by each of the terms inside. In this case, we need to multiply negative nine by five and negative nine by negative six 𝑥. In order to work out these two calculations, we need to remember some rules of multiplying positive and negative numbers. When we multiply two positive numbers or two negative numbers, we get a positive answer. Whereas when we multiply a positive by a negative or a negative by a positive, we get a negative answer.

Nine multiplied by five is equal to 45. Therefore, negative nine multiplied by five is equal to negative 45. Negative nine multiplied by negative six will give us positive 54. This means that negative nine multiplied by negative six 𝑥 is equal to 54𝑥. The expression that is equivalent to negative nine multiplied by five minus six 𝑥 is negative 45 plus 54𝑥. This was option A out of our five choices.

We could also have answered this question by factorizing each of our five options and see which one was equal to negative nine multiplied by five minus six 𝑥. Negative 45 and 54𝑥 have a common factor of negative nine. This means that we can take this outside of the parentheses. Negative 45 divided by negative nine is equal to five. Therefore, the first term inside the parentheses is five. 54𝑥 divided by negative nine is equal to negative six 𝑥. So, this is the second term inside the parentheses. As this is the expression that we started with, we know that our answer, negative 45 plus 54𝑥, is correct.