Comparing absolute values on number line  Negative numbers  6th grade  Khan Academy  Summary and Q&A
TL;DR
This video explains how to determine the truth of inequalities involving absolute values using number line plots.
Questions & Answers
Q: How can we determine if "a is less than b" is true based on a number line plot?
To determine if "a is less than b" is true, we look at the positions of a and b on the number line. If a is to the left of b, then a is indeed less than b. This is because the number line increases from left to right.
Q: Why is the absolute value of a not greater than the absolute value of b?
The absolute value of a represents the distance from a to zero. In the given number line plot, a is three hash marks to the left of zero, while b is eight hash marks to the right of zero. Since the absolute value of a is to the left of the absolute value of b, it is not greater.
Q: How can we determine if "the absolute value of a is less than the absolute value of c" is true?
By comparing the positions of a and c on the number line, we can see that the absolute value of a is equal to the absolute value of c. Therefore, the statement "the absolute value of a is less than the absolute value of c" is false.
Q: Why is "a is less than c" true in the given number line plot?
Since a is to the left of c on the number line, it is indeed less than c. The number line increases from left to right, so any number to the left of another number is smaller.
Summary & Key Takeaways

This video walks through four inequalities involving absolute value and explains how to determine their truth based on the given number line plot.

The first inequality, "a is less than b," is true because a is to the left of b on the number line.

The second inequality, "the absolute value of a is greater than the absolute value of b," is false because the absolute value of a is to the left of the absolute value of b on the number line.

The third inequality, "the absolute value of a is less than the absolute value of c," is false because the absolute value of a is equal to the absolute value of c.