Which conjunction or disjunction equivalent to the open sentence 4 –3|n + 2| ≥ 1?

A.

n + 2 ≥ 1 and n + 2 ≤ –1

B.

n + 2 ≤ 1 and n + 2 ≥ –1

C.

n + 2 ≤ 1 and n − 2 ≥ −1

D.

n + 2 ≥ 1 or n – 2 ≤ 1

Question

Which conjunction or disjunction equivalent to the open sentence 4 –3|n + 2| ≥ 1?
  
 
 

 

 
  

  A. 
 
n + 2 ≥ 1 and n + 2 ≤ –1
   
   

 

 
  

  B. 
 
n + 2 ≤ 1 and n + 2 ≥ –1
   
   

 

 
  

  C. 
 
n + 2 ≤ 1 and n − 2 ≥ −1
  
   

 

 
  

  D. 
 
n + 2 ≥ 1 or n – 2 ≤ 1

zzr0ck3r · Answer

$4-3|n+2|\ge 1$

 first subtract $4$ from both sides

$-3|n+2|\ge -3$

then divide by $-3$ remembering to flip the sign

$|n+2|\le 1$

zzr0ck3r · Answer

with me?

anonymous · Answer

yes

zzr0ck3r · Answer

$|a|\le b \implies -b\le a \le b $

so we have 

$|n+2|\le 1 \implies -1\le n+2\le 1 \implies -3\le n \le -1$

so $n\le -1$     AND     $-3\le n$

zzr0ck3r · Answer

you can actually stop at $-1\le n+2 \le 1$ this implies $n+2 \le 1$ and $-1\le n+2$