1. Fill in each with =, <, or >to make a true statement.
a. (-5)+(-21)| O|-5|+|-21|
c. (-187) + 50|O-187|+|50|
b. (-47) +47) O-47|+|47|
d. (-88) + 127|O-88|+|127|
On the basis of your answers above, write a general rule for a + b) O lal + b) that holds true for all numbers a and b. Explain why this rule is true.
a. (-5)+(-21)| O|-5|+|-21|
c. (-187) + 50|O-187|+|50|
b. (-47) +47) O-47|+|47|
d. (-88) + 127|O-88|+|127|
On the basis of your answers above, write a general rule for a + b) O lal + b) that holds true for all numbers a and b. Explain why this rule is true.
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Answer:
a. (-5) + (-21) < |-5| + |-21|
b. (-47) + 47 = |-47| + |47|
c. (-187) + 50 < |-187| + |50|
d. (-88) + 127 < |-88| + |127|
Step-by-step explanation:
General Rule: For any two numbers a and b, the expression (a + b) is always less than or equal to the absolute value of the sum of the absolute values of a and b.
Explanation: This rule is true because the absolute value function returns the non-negative value of a number. Therefore, when we add the absolute values of a and b, we are essentially adding their magnitudes. The sum of the magnitudes is always greater than or equal to the sum of the original numbers, because it accounts for any negative values. So, (a + b) will always be less than or equal to the absolute value of the sum of the absolute values of a and b.