Question

Which of the following expressions are equivalent to 5(-2k-3) = 2k?

A) (-5 * 3) - 8k
B) 15
C) None of the above
D) All of the above

Answer 1

To find the equivalent expressions, distribute the number outside the parentheses, combine like terms, and simplify the equation. Then substitute the value of k into each given expression to determine which ones are equivalent to the original equation. The answer is C) None of the above.

Step-by-step explanation:

In order to find the equivalent expressions, we need to simplify the given expression.

First, distribute the 5 to each term inside the parentheses: 5 * -2k = -10k and 5 * -3 = -15.

Therefore, the original equation becomes -10k - 15 = 2k. Next, combine like terms by adding 10k to both sides: -10k + 10k - 15 = 2k + 10k.

This simplifies to -15 = 12k. To solve for k, divide both sides by 12: -15/12 = k.

Simplifying further, k = -5/4.

Now, let's substitute the value of k into each given expression to see which ones are equivalent to the original equation. A) (-5 * 3) - 8k = (-15) - (-5/4 * 8) = -15 - (-10) = -5.

This is not equal to 2k. B) 15 is not equal to 2k. Therefore, the answer is C) None of the above.