Explain what it means algebraically for an equation to
have infinite solutions.
An equation has infinite solutions if there are an unlimited number of values that can satisfy the equation. This typically occurs when the equation is true for any value of the variable(s) involved. In other words, the equation does not restrict the possible solutions in any way, resulting in an infinite number of solutions.
Algebraically, this can be represented by a statement such as "0 = 0" or "x = x" where the variable can be any real number. This means that no matter what value you substitute for the variable, the equation will always be true. In cases like this, the equation is said to have infinite solutions because there are no limitations on what values can satisfy it.