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Which expressions are equivalent to [5 (-3)(6x-5)]?

1) [18x-20]
2) [3x-3]
3) none of the above

User Jkasten
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1 Answer

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Final answer:

The expression equivalent to 5 (-3)(6x-5) is -90x + 75, which means that the correct answer is 'none of the above' as neither [18x-20] nor [3x-3] matches the resulting expression.

Step-by-step explanation:

The expression 5 (-3)(6x-5) involves using the rules of signs for multiplication. To find the equivalent expression, we should first multiply the constants 5 and -3, then distribute the resulting product through the parentheses (6x-5).

Multiplying 5 and -3 results in a product with a negative sign, following rule #6 that when two numbers with the same sign are multiplied, the result is positive, but in this case, since we are multiplying a positive by a negative, according to rule #7, the result is negative.

5 (-3) = -15

Now, we distribute -15 through (6x-5):

  • -15 × 6x = -90x
  • -15 × (-5) = +75

Combining these products, we get the expression -90x + 75.

Thus, none of the provided options 1) [18x-20] or 2) [3x-3] are equivalent to 5 (-3)(6x-5). The correct choice is 3) none of the above.

User Gus
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