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Answer:
The following statements are true
(2)(6) > (–2)(2)
6/-2 < -2/-2
6/2 > -2/2
Step-by-step explanation:
Missing options
(2)(6) > (–2)(2)
6/2 < -2/2
(–2)(6) > (–2)(–2)
6/-2 < -2/-2
(2)(6) < (–2)(2)
6/2 > -2/2
Before we know which statement is true, you must understand that when both sides of an inequality is multiplies or divided by a negative number, the inequality sign reverses.
For the first option:
6 > -2
Multiplying both sides by 2 will not reverse the inequality sign
Hence 2(6)>2(-2) is true since the inequality was retained.
For the second option:
6/2 < -2/2
Dividing both sides by 2 will not reverse the inequality sign
Hence 6/2>2/2 is true nullifying the given expression 6/2 < -2/2 . Hence this expression is false
For the third option:
(–2)(6) > (–2)(–2)
Both sides were multiplied by a negative number i.e -2. Hence the sign supposed to reverse because -12 > 4 is false therefore this expression is FALSE
For the fourth option
6/-2 < -2/-2
Both sides were divided by a negative number i.e -2. Hence the sign supposed to reverse because -3 < 1 is true, therefore this expression is TRUE
For the fifth option:
((2)(6) < (–2)(2)
Both sides were multiplied by a positive number i.e 2. Hence the sign is not supposed to reverse because 12 < -4 is False, therefore this expression is FALSE
For the sixth option:
6/2 < (–2)/2
Both sides were divided by a positive number i.e 2. Hence the sign is not supposed to reverse because 3 < -4 is TRUE, therefore this expression is TRUE