Question

Question 5 (Essay Worth 4 points) Create your own two-step equation with NO SOLUTION as the solution. Show the steps to solving the equation and explain in words why your work proves that there are NO SOLUTIONS.

Answer 1

So when you get no solution, usually it's because you get two different constants that are equal to each other. So the variable in your original equation has to at some point be cancelled out. Since this is two steps, we need to add another step. Let's just throw a distributive property in here.

So let's say we have:
3(x+2) = 3x-2
(1) 3x+6=3x-2
(2) 6=-2

since (2) is false and the two constants are not equal, the equation has no solution.