To solve the equation 3x + 5 = 2x + 7, we will follow these steps:
1. First, our goal is to isolate x on one side of the equation to find its value. It's often easiest to get x terms on one side and constants on the other.
2. We currently have x terms on both sides of the equation (3x on the left and 2x on the right). To combine them, we can subtract 2x from both sides of the equation:
3x + 5 - 2x = 2x + 7 - 2x
3. Simplify both sides of the equation:
(3x - 2x) + 5 = (2x - 2x) + 7
x + 5 = 7
4. Now we have an equation with x on one side and numbers on the other, but we need to isolate x completely. To do this, let's subtract 5 from both sides to get rid of the constant term next to x:
x + 5 - 5 = 7 - 5
5. Simplify the equation:
x = 2
So, the solution is x = 2.
None of the other options (infinite number of solutions, no solutions, x = 0, or 2x) apply to the given equation. The correct choice is x = 2, and this is a single, unique solution.
