Answer and Step-by-step explanation:
To determine the number of solutions for the equation 1.5(x+4)-3=4.5(x-2), we can simplify and solve the equation:
1. Distribute the multiplication to simplify the equation:
1.5x + 6 - 3 = 4.5x - 9
2. Combine like terms:
1.5x + 3 = 4.5x - 9
3. Move the variables to one side of the equation by subtracting 1.5x from both sides:
3 = 3x - 9
4. Move the constant term to the other side of the equation by adding 9 to both sides:
3 + 9 = 3x - 9 + 9
5. Simplify:
12 = 3x
6. Divide both sides of the equation by 3 to isolate x:
12/3 = 3x/3
7. Simplify:
4 = x
After solving the equation, we find that x equals 4. Therefore, there is only one solution for the given equation: x = 4.