Comparing absolute values on number line | Negative numbers | 6th grade | Khan Academy

TL;DR

This video explains how to determine the truth of inequalities involving absolute values using number line plots.

Transcript

• [Voiceover] What I have here are three numbers plotted on the number line. We have the number a, the number c, the number b. And then we have three -- (laughs) we have four inequalities, actually. Four inequalities that involve absolute value. And what I want to do is figure out which is these inequalities are true, given where a, c and b are on ... Read More

Key Insights

• 🫥 Inequalities involving absolute value can be visualized and analyzed using number line plots.
• #️⃣ To determine the truth of an inequality, compare the positions of the numbers on the number line.
• #️⃣ Absolute value represents the distance of a number from zero, and positive numbers have the same absolute value as their corresponding negative numbers.

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.