Give an explanation on how many solutions this equation has? 7x + 3 = 7x + 3
The equation 7x + 3 = 7x + 3 has an infinite number of solutions. This is because the equation is an identity, meaning that the expression on the left-hand side (LHS) is exactly the same as the expression on the right-hand side (RHS). No matter what value of x you choose, the equation will always hold true because both sides are identical.
To see why this is the case, you can subtract 7x from both sides of the equation, which would give you:
7x + 3 - 7x = 7x + 3 - 7x
Simplifying both sides gives you:
3 = 3
This is obviously a true statement for all values of x. Since there is no x term left after simplifying, and you're left with a true statement, it means that x can be any real number and the original equation will still be true. Therefore, the equation has an infinite number of solutions.