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24. Consider the equation.

6(x-1(-5=2x-3
Which statement about a possible first step to solve the equation is true?
A. the equation can be rewritten as 6x -6 =2x-3 using the distributive property
B.the equatuioncan be rewritten as 6x-1-5=2x-3 using the distributive property
C.the equation can be rewritten as 6(x-1)=2x-8 using the distrbutive property
D. the equation can be rewritten as 6(x-1)=2x+2 using the distributive property.

1 answer

To solve the equation \(6(x - 1(-5) = 2x - 3\), we first need to simplify the expression correctly.

Here, it seems that the equation might have a typo, as \(1(-5)\) seems unusual. If we assume that it was meant to be \(6(x - 1) = 2x - 3\), let's explore the options with that assumption.

The equation can be rewritten using the distributive property as follows:

  1. Distributive Property: The distributive property states that \(a(b + c) = ab + ac\). In the context of our equation, we apply this to \(6(x - 1)\): \[ 6(x - 1) = 6x - 6 \]

Now we can analyze the provided options:

  • A: The equation can be rewritten as \(6x - 6 = 2x - 3\) using the distributive property. (TRUE)

  • B: The equation can be rewritten as \(6x - 1 - 5 = 2x - 3\) using the distributive property. (FALSE)

  • C: The equation can be rewritten as \(6(x - 1) = 2x - 8\) using the distributive property. (FALSE)

  • D: The equation can be rewritten as \(6(x - 1) = 2x + 2\) using the distributive property. (FALSE)

Thus, the correct answer is A: The equation can be rewritten as \(6x - 6 = 2x - 3\) using the distributive property.