Question

Write a related function for 6x−3x−2=7.

Answer 1

To write a related function for the equation \( 6x - 3x - 2 = 7 \), we first simplify the equation:

1. Combine like terms:
\[
6x - 3x - 2 = 3x - 2
\]

2. Set the equation equal to 7:
\[
3x - 2 = 7
\]

Next, let's create a function that represents the left side of the equation. We can define a function \( f(x) \) as follows:

\[
f(x) = 3x - 2
\]

Now, in order to find \( x \) when \( f(x) = 7 \), we can solve the equation \( f(x) = 7 \):

\[
3x - 2 = 7
\]

This is a function related to the original equation \( 6x - 3x - 2 = 7 \), and it allows us to find the value of \( x \) that satisfies the equation.

Finally, to solve for \( x \):

1. Add 2 to both sides:
\[
3x = 9
\]

2. Divide both sides by 3:
\[
x = 3
\]

Thus, the related function is \( f(x) = 3x - 2 \) and the solution to the equation \( 6x - 3x - 2 = 7 \) is \( x = 3 \).