Let A = {x: x 3x=6}. Does A?
My answer: A ≠ 2 because x = 2 and x is an element of set A. Thus, A = {2}, but A itself is not equal to 2.
{x: x 3x=6} ??
Do you mean {x: 3x=6} ??
Then you ask
Does A?
Does A what?
However, you are correct in saying that {2} is not 2
Yes, I meant A = {x: 3x=6}. Is A therefore equal to 2, or is x = 2 just, instead of A = 2?
x = 2
A = {2}
Thank you. X = 2 and A = {2} makes sense. But let's say that A IS equal to 2. Could you explain how A could be equal to 2? I don't think it's possible. Maybe, if A contained two elements, then we could say that n(A) = 2.
Well, A is not a person, so it doesn't have a personal preference like "Does A?" But if you're asking if A equals 2, then the answer is yes! As you correctly pointed out, A is the set of all x values such that 3x equals 6. And lo and behold, when we plug x = 2 into the equation, we get 3(2) = 6. So, A = {2}. Just remember, A is not 2, it's a set containing 2. It's like saying "I have a clown in my pocket," but you're not a pocket!
You are correct in saying that A does not equal 2. However, let me explain the steps you can take to solve this equation and find the value of x that belongs to set A.
The given equation is 3x = 6. To solve for x, you can follow these steps:
Step 1: Start with the equation 3x = 6.
Step 2: Divide both sides of the equation by 3 to isolate x. This gives us x = 2.
Step 3: Check if the value of x satisfies the original equation. Substituting x = 2 into the equation, we get 3(2) = 6, which is true.
Step 4: Since x = 2 satisfies the equation, the value of x belongs to set A.
Step 5: Therefore, we can conclude that the set A is equal to {2}.
So, A is a set containing only the element 2, which is written as A = {2}. However, it's important to note that A itself is not equal to 2.