How do you solve and graph #abs(n+5)=3#?

Question

How do you solve and graph #abs(n+5)>=3#?

Kennedy Adams · Accepted Answer

#-8>=n# OR #n>=-2#

(the reds)
#color(red)(-----(-8))#--------#color(red)((-2)----0---->)#n

Solve: #abs(n+5)>=3# #=># #-3>=n+5# OR #n+5>=3# #=># #-8>=n# OR #n>=-2# Graph: On n axis: -------------0------------->n We put #n=-8# , #n=-2# ----------#color(red)((-8))#--------#color(red)((-2))#----0------------->n We need #-8>=n# OR #n>=-2# (the reds) #color(red)(-----(-8))#--------#color(red)((-2)----0---->)#n

Abigail Allen · Answer

undefined To solve the absolute value inequality $ |n + 5| \geq 3 $, you'll need to consider two cases:

1. $ n + 5 \geq 3 $  
2. $ -(n + 5) \geq 3 $

Solve each case separately to find the values of $ n $. Then, graph the solution on a number line.

1. For the first case, $ n + 5 \geq 3 $, subtract 5 from both sides to get $ n \geq -2 $.

2. For the second case, $ -(n + 5) \geq 3 $, distribute the negative sign and solve for $ n $, which gives $ -n - 5 \geq 3 $. Add 5 to both sides and then multiply both sides by -1 (to reverse the inequality when multiplying by a negative number), yielding $ n \leq -8 $.

Thus, the solution is $ n \leq -8 $ or $ n \geq -2 $. On the number line, graph a closed circle at -8 and -2, then shade to the left of -8 and to the right of -2.

How do you solve and graph #abs(n+5)&gt;=3#?

How do you solve and graph #abs(n+5)>=3#?