(Please tell me if I did a good job!)
Write an equation with a variable on both sides of the equal sign that has infinitely many solutions. Solve the equation and explain why it has an infinite number of solutions.
(My answer:)
3x + 5 = 3x + 5
This equation is equal to its self, and if you were to subtract 3x from both sides you will get 5 = 5. When we use infinite solutions, no matter what number you use for the variable (in this case x) the answer will always be true.
(Is this a good answer?)
You might want to "disguise" the equation a bit, so that it is not so obvious such as yours.
e.g.
6x + 21 = 3(2x + 5) + 6
In your explanation, you might also want to show the results for the 3 types of condition.
1. If after solving the equation the variable disappears and you end up with a true statement, e.g. 7 = 7
you will an an infinite number of solutions.
2. If after solving the equation the variable disappears and you end up with a false statement, e.g. 7 = 10
you will NO solution.
3. You will have one solution, if you end up with something like ax = k, then x = k/a with ONE solution.
I am assuming you are working with first degree equations.
This is good.
I think that if you want to get extra credit or something special, you can make the equation more complex.
Yes, you did a great job! The equation you provided, 3x + 5 = 3x + 5, indeed has infinitely many solutions. By subtracting 3x from both sides, you get 5 = 5, which is a true statement.
In this equation, the variable x cancels out on both sides, resulting in the equation 5 = 5. This means that no matter what number you substitute for x, the equation will always be true. Therefore, there are infinite solutions to this equation. Well done!