Question

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

Answer 1

To solve the equation \( 2x + 3 = 3x + 4 \) using function graphs, we can visualize both sides of the equation as separate functions:

1. Define the function from the left side of the equation:
\[
f(x) = 2x + 3
\]

2. Define the function from the right side of the equation:
\[
g(x) = 3x + 4
\]

Next, we need to find the x-value(s) where these two functions intersect, which means solving the equation \( f(x) = g(x) \).

To determine the solution algebraically:

1. Set the equations equal:
\[
2x + 3 = 3x + 4
\]

2. Rearrange the equation:
\[
2x - 3x = 4 - 3
\]
\[
-x = 1
\]

3. Multiply by -1:
\[
x = -1
\]

Now, we can check if \( x = -1 \) satisfies the original equation:

- Left side:
\[
2(-1) + 3 = -2 + 3 = 1
\]

- Right side:
\[
3(-1) + 4 = -3 + 4 = 1
\]

Since both sides are equal when \( x = -1 \), the solution to the equation \( 2x + 3 = 3x + 4 \) is:

\[
\boxed{-1}
\]

So the correct response from the options given is \( -1 \).