A student wrote – 3 > x > 5 as the inequality that represents the real numbers less than – 3 or greater than 5. Explain why this is incorrect.
here in the question
x<-3 means x={-4,-5,-6,....}
x>5 means x={6,7,8,....}
there is no x such that it is less than -3 and greater than 5
hence the representation is incorrect
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The inequality -3 > x > 5 is incorrect for representing the real numbers less than -3 or greater than 5. To understand why it's incorrect, let's break it down.
First, let's consider the statement -3 > x. It means that -3 is greater than x. However, we know that the student intended to represent the real numbers less than -3. Therefore, the correct statement should be x < -3, where x is less than -3.
Next, let's look at the statement x > 5. This part implies that x is greater than 5, but the student intended to represent the real numbers greater than 5. The correct statement would be x > 5, where x is greater than 5.
To combine these statements in a correct way, we use the union symbol (∪) to represent "or." Therefore, the corrected inequality should be x < -3 ∪ x > 5, which means x is either less than -3 OR greater than 5.
In summary, the student's original inequality mistakenly used the greater than symbol instead of less than symbol, and vice versa. The correct representation should use the less than symbol for numbers less than -3 and the greater than symbol for numbers greater than 5, combining them with the union symbol (∪).