Which conjunction or disjunction is equivalent to the open sentence |a – 8| ≤ 3.

A.

a – 8 ≤ 3 and a – 8 ≥ –3

B.

a – 8 ≥ 3 and a – 8 ≤ –3

C.

a – 8 ≤ 3 or a – 8 ≥ –3

D.

a – 8 ≥ 3 or a – 8 ≤ –3

Question

Which conjunction or disjunction is equivalent to the open sentence |a – 8| ≤ 3.
	
	
 
A.
	

a – 8 ≤ 3 and a – 8 ≥ –3
	
 
B.
	

a – 8 ≥ 3 and a – 8 ≤ –3
	
 
C.
	

a – 8 ≤ 3 or a – 8 ≥ –3
	
 
D.
	

a – 8 ≥ 3 or a – 8 ≤ –3

tkhunny · Answer

It's "and".  That eliminates two choices.

Why would it be <3 with the absolute values but >3 without them?  This eliminates the rest of the confusion.

anonymous · Answer

i dont really get it

tkhunny · Answer

$|a-8|\le 3$

This is equivalent to

$-3 \le a-8 \le 3$

anonymous · Answer

ok..but i dont see that in the answers?

tkhunny · Answer

That's because it is written as a conjunction, rather than a compound inequality.

You should find the equivalent expression $-3 \le a-8\; AND\;a-8 \le 3$

anonymous · Answer

can you try explaining how to find the answer for questions like this?

tkhunny · Answer

It easy enough with ONE concept.

|something| < is a Conjunction -- Two regions that overlap and we want the intersection.
|something| > is a Disjunction -- Two regions that do not overlap and we want both pieces.