Question

Use the function graphs to solve the equation 2x+3=3x+4 . (1 point) Responses 2 2 1 1 −1 negative 1 7

Answer 1

To solve the equation \(2x + 3 = 3x + 4\) using function graphs, we can rearrange this equation into a form where we can analyze it as two functions.

Let's set the equation equal to zero:

\[
2x + 3 - 3x - 4 = 0 \implies -x - 1 = 0 \implies x = -1
\]

This tells us that the solution to the equation is \(x = -1\).

If we want to visualize it using function graphs, we can consider these two functions:

1. \(f(x) = 2x + 3\)
2. \(g(x) = 3x + 4\)

Now, to find the solution graphically, we would find the intersection of the two functions. The point where these two graphs intersect would be the solution to the equation \(2x + 3 = 3x + 4\).

As we determined algebraically, the solution where the two functions intersect would indeed be at \(x = -1\).

So the response to the question is:

\(-1\)