Final answer:
The equation 5x-2=3+5(x-1) simplifies to -2 = -2, demonstrating that the equation is true for all values of x, meaning it has an infinite number of solutions.
Step-by-step explanation:
Solving the Algebraic Equation-
To solve the equation 5x−2=3+5(x−1), we need to follow algebraic steps and simplify. First, distribute the 5 on the right side of the equation:
5x − 2 = 3 + 5x − 5
Next, we simplify the right side by combining like terms:
5x − 2 = 5x − 2
Now, by subtracting 5x from both sides, we notice that the x terms cancel out:
5x − 5x − 2 = 5x − 5x − 2
This results in:
− 2 = − 2
Since both sides of the equation are equal, this tells us that the equation is true for all values of x. In other words, x can be any real number. Therefore, this equation has an infinite number of solutions. It's important to check your answer to ensure it is reasonable, which we have done during the simplification process.