Use the image to answer the question.

Question

Two lines slope upward on a coordinate plane. A solid line passes through the plotted point left parenthesis 2 comma 7 right parenthesis. A dotted line intersects the first line at the plotted point left parenthesis negative 1 comma 1 right parenthesis.

Use the function graphs to solve the equation 2x+3=3x+4 .

(1 point)
Responses

−1
negative 1

7
7

1
1

2

Answer 1

To solve the equation 2x + 3 = 3x + 4, we first need to isolate x on one side of the equation.

Subtract 3 from both sides:
2x + 3 - 3 = 3x + 4 - 3
2x = 3x + 1

Now subtract 3x from both sides:
2x - 3x = 3x + 1 - 3x
-x = 1

Since we want to find the value of x, we can multiply both sides of the equation by -1 to get rid of the negative sign:
-x * -1 = 1 * -1
x = -1

Therefore, the solution to the equation 2x + 3 = 3x + 4 is x = -1. This aligns with the coordinates given in the image, where the dotted line intersects the solid line at the point (-1, 1).