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.