Final answer:
The equation 5y+2 = (1/2)(10y+4) has infinitely many solutions.
Step-by-step explanation:
To determine the number of solutions for the equation 5y+2 = (1/2)(10y+4), we can start by simplifying the equation:
5y + 2 = 5y + 2
Since the equation is the same on both sides, it means that the equation is an identity and therefore has infinitely many solutions. This means that no matter what value of y we substitute into the equation, it will always be true.
Start by distributing the 1/2 on the right side of the equation:
5y + 2 = 1/2 * 10y + 1/2 * 4
5y + 2 = 5y + 2
When we simplify both sides, we see that they are identical, indicating that the equation is true for all values of y. Hence, the equation has infinitely many solutions. This means that any value for y will satisfy the equation.