Question

problem 7
a. make a true inequality by dragging the cards.
b. explain how you know your inequality is true.

Explanation:

Part (a)

Step1: Recall absolute value

The absolute value of a number \( x \), denoted \( |x| \), is its distance from 0 on the number line, so \( |x| \geq 0 \) for all real \( x \), and \( |x| = |-x| \). For example, \( |-2| = 2 \), \( |-1| = 1 \), \( |1| = 1 \), \( |2| = 2 \).

Step2: Choose numbers for inequality

Let's pick \( | -2 | \) for the left box and \( 1 \) for the right box. So the inequality is \( | -2 | > 1 \). (Other valid options: \( | -2 | > -1 \), \( |2| > 1 \), \( |2| > -1 \), \( | -1 | > -2 \), \( |1| > -2 \), etc.)

Part (b)

Step1: Calculate absolute value

First, calculate the absolute value of the left - hand side. If we take the inequality \( | -2 | > 1 \), we know that by the definition of absolute value, \( | -2 | = 2 \) because the distance of - 2 from 0 on the number line is 2.

Step2: Compare the two numbers

Then we compare 2 and 1. Since 2 is greater than 1 (because 2 - 1=1>0), we can conclude that \( | -2 | = 2>1 \), so the inequality \( | -2 | > 1 \) is true.

Answer:

(Part a):
\( | -2 | > 1 \) (or other valid inequalities like \( | -2 | > -1 \), \( |2| > 1 \), \( |2| > -1 \), \( | -1 | > -2 \), \( |1| > -2 \))