Explain the difference in meaning between |−7| and −7. In your explanation, be sure to include various key words you learned within this unit.
In this unit, we have learned about absolute value and negative numbers. The absolute value of a number is the distance of that number from zero on a number line, without considering its sign. It is represented by the notation |x|.
Now, let's apply this understanding to the difference between |−7| and −7. |−7| represents the absolute value of -7, which means we only consider the distance from zero, regardless of the negative sign. In this case, the absolute value of -7 is simply 7 because -7 is 7 units away from zero on the number line.
On the other hand, -7 itself represents a negative number. Negative numbers are less than zero and are represented by a negative sign placed in front of a number. In this case, -7 represents the specific number -7, which is a value that is less than zero and does not consider the distance from zero.
In summary, the main difference between |−7| and −7 is that |−7| represents the absolute value of -7, which calculates the positive distance from zero, while -7 represents the negative number itself, with no consideration for the distance.