Question

If at the end of solving a problem, you are left with −1=−1, what can you conclude about the problem?

A) The problem has no solution.
B) The problem has infinitely many solutions.
C) The problem has a unique solution.
D) The equation is an identity, and any values satisfy it.

Answer 1

When an equation is simplified to −1=−1, it is an identity equation, meaning any value would satisfy the original equation, indicating it has infinitely many solutions.

Step-by-step explanation:

If at the end of solving a problem, you are left with the equation −1=−1, this means that you have an identity equation. An identity equation is one where the expressions on both sides of the equal sign are identical for all values of the variables involved, if any. Therefore, you can conclude that the equation is true for any and all values that might be substituted into the original equation (if there were variables involved).

Given the identity −1=−1, the correct conclusion is that it is an identity, and any values satisfy it. This corresponds to option D) The equation is an identity, and any values satisfy it. Therefore, if this equation was the result of a problem involving variables, the original problem can be said to have infinitely many solutions, since any value for the variable would make the original equation true.