-3 > x > 5 as the inequality that represents the real numbers less than -3 or greater than 5. Explain why this is incorrect.
x is to the left of negative 3 and to the right of positive 5.
That would require a circular number line :)
All real numbers that are between -1 and 4
Well, well, well, looks like we have a little math problem here! Let's give it a go, shall we?
The inequality -3 > x > 5 is indeed incorrect. Here's why: when we have a compound inequality like this, we have to make sure that both parts make sense individually.
Let's start with the first part, -3 > x. This means that x is less than -3. So far, so good! However, the second part, x > 5, tells us that x is greater than 5. Uh-oh, that's a problem!
You see, my friend, we can't have x be less than -3 and greater than 5 at the same time. It's like saying you want to eat pizza and broccoli at the same time. Sure, you might be a lover of strange food combinations, but math just doesn't work that way!
So, the correct way to represent the real numbers less than -3 or greater than 5 is actually written as x < -3 or x > 5. It's as simple as that! Now, go forth and conquer those inequalities, my friend!
The given inequality, "-3 > x > 5," incorrectly represents the real numbers that are less than -3 or greater than 5.
To understand why it is incorrect, let's break it down and analyze each part separately:
1. "-3 > x": This part implies that x is less than -3. It means that x should be a number smaller than -3.
2. "x > 5": This part implies that x is greater than 5. It means that x should be a number larger than 5.
The issue with "-3 > x > 5" is that it tries to represent a number that is smaller than -3 and also larger than 5 simultaneously. In reality, there is no number that can satisfy both conditions at the same time. This is why the given inequality is incorrect and does not accurately represent the real numbers that are less than -3 and greater than 5.
To properly represent the real numbers that are less than -3 or greater than 5, we should use the logical operator "or" (represented by the symbol "∨") instead of the logical operator "and" (represented by the symbol "∧").
The correct inequality would be: x < -3 ∨ x > 5