Final answer:
The equation 3x + 2 = 2x - 3 has one solution on the number line and in the Cartesian plane.
Step-by-step explanation:
To find the solutions of the equation 3x + 2 = 2x - 3, we need to simplify and solve for x. Subtracting 2x from both sides gives us x + 2 = -3. Then, subtracting 2 from both sides gives us x = -5. So, there is one solution for the equation on the number line.
In the Cartesian plane, the equation represents a linear function. Since the slope of the line is the coefficient of x, which is 3, and the y-intercept is the constant term, which is 2, the line will not intersect itself. Therefore, there is one solution for the equation in the Cartesian plane as well.
Learn more about Solving linear equations