Question

Using the equation `C=5+12x,`which of the following statements could be a correct interpretation of the coefficient of a term?

#3.
Which of the following statements about the equation 3x−1=7+x is correct?

Answer 1

To address your first question regarding the equation \( C = 5 + 12x \), the coefficient of the term \( x \) is \( 12 \). This means that for every unit increase in \( x \), the value of \( C \) increases by \( 12 \) units. A correct interpretation of the coefficient \( 12 \) is that it represents the rate of change of \( C \) with respect to \( x \).

As for your second question regarding the equation \( 3x - 1 = 7 + x \), here's how you can interpret it:

To solve the equation, you would follow these steps:

1. Combine like terms and isolate \( x \):
\[
3x - x = 7 + 1
\]
\[
2x = 8
\]

2. Divide both sides by \( 2 \):
\[
x = 4
\]

So, the statement that would be correct in relation to the equation \( 3x - 1 = 7 + x \) could be that the solution to the equation is \( x = 4 \).

If you need more specific interpretations or additional statements regarding these equations, please provide them!