Question

use the following number line to determine if the expressions are true or false.
(number line with points a (blue), b (pink), and 0, a is left of b, both left of 0)
true false
$a < b$ $\circ$ $\circ$
$|a| < |b|$ $\circ$ $\circ$
$|a| < b$ $\circ$ $\circ$

Explanation:

Step1: Analyze \( a < b \)

On the number line, numbers to the left are smaller. \( a \) is left of \( b \), so \( a < b \) is true.

Step2: Analyze \( |a| < |b| \)

\( a \) is farther from 0 than \( b \), so \( |a| > |b| \). Thus, \( |a| < |b| \) is false.

Step3: Analyze \( |a| < b \)

\( b \) is negative (left of 0), \( |a| \) is positive. Positive > negative, so \( |a| < b \) is false.

Answer:

• \( a < b \): True (select True circle)
• \( |a| < |b| \): False (select False circle)
• \( |a| < b \): False (select False circle)