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 \( -1 \).