Question

Are the two solutions to x (2x+1) = 1 found by setting x = 1 and 2x + 1 = 1? Explain your reasoning. What are the solutions to this equation? Show how you arrived at your answer. Create an equation for your classmates to solve that requires factoring.

Answer 1

nope. Just because two numbers multiply together to make 1, you still know nothing about the numbers.

If nothing else, try your idea.
If x=1, 2x+1=3, and 1*3≠1

However, if two numbers multiply to be zero, then one or the other must be zero. So, let's set things equal to xero, rather than 1.

x(2x+1) - 1 = 0
2x^2 + x - 1 = 0
you can factor that to get
(2x-1)(x+1) = 0

Now you have two possibilities:
2x-1 = 0
x+1 = 0

So, that gives you two solutions for x:
x = 1/2
x = -1

To verify that they satisfy the original equation, plug them in:

(1/2)(1+1) = 1
(-1)(-1) = 1

So we are good.