Question

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.

Answer 1

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.