Question

Please help!!! How do I explain this?

Task: Determine whether each statement is always, sometimes, or never true. Explain.

Answer 1

The statement "If a and b are integers and a > b, then lal > Ibl" is true.

Step-by-step explanation:

• |a| represents the absolute value of a, which is the distance of a from zero on the number line
• Since a is greater than b (a > b), a is further away from zero on the number line than b
• Therefore, |a| must be greater than |b|
• This can be written as: |a| > |b|
• Since a and b are integers, their absolute values will always be positive integers
• Therefore, we can drop the absolute value signs, and the statement can be written as: |a| > |b| becomes a > b
• This means that the magnitude of a (i.e., |a|) is greater than the magnitude of b (i.e., |b|)
• So, the statement "If a and b are integers and a > b, then lal > Ibl" is true