Question 145954
Let's solve {{{x+8<-6}}}





{{{x+8<-6}}} Start with the first inequality



{{{x<-6-8}}}Subtract 8 from both sides



{{{x<-14}}} Combine like terms on the right side



So the first part of our answer is {{{x<-14}}} 



Here's the graph of the solution set


{{{drawing(500,80,-24, -4,-10, 10,
number_line( 500, -24, -4),


arrow(-14,0,-24,0),
arrow(-14,0.30,-24,0.30),
arrow(-14,0.15,-24,0.15),
arrow(-14,-0.15,-24,-0.15),
arrow(-14,-0.30,-24,-0.30),




circle(-14,0,0.3),
circle(-14,0,0.3),
circle(-14,0,0.3),
circle(-14,0,0.3-0.02)
)}}}



-------------


Now let's solve {{{x+8>3}}}


{{{x+8>3}}} Start with the given inequality




{{{x>3-8}}}Subtract 8 from both sides



{{{x>-5}}} Combine like terms on the right side


So the second part of our answer is {{{x>-5}}} 


Here's the graph of the solution set


{{{drawing(500,80,-15, 5,-10, 10,
number_line( 500, -15, 5),

arrow(-5,0,5,0),
arrow(-5,0.30,5,0.30),
arrow(-5,0.15,5,0.15),
arrow(-5,-0.15,5,-0.15),
arrow(-5,-0.30,5,-0.30),

circle(-5,0,0.3),
circle(-5,0,0.3),
circle(-5,0,0.3),
circle(-5,0,0.3-0.02)


)}}}




-----------------------Solution


So the answer is 


{{{x<-14}}} or {{{x>-5}}} 


which looks like



{{{drawing(500,80,-18, 3,-10, 10,
number_line( 500, -18, 3),

arrow(-5,0,3,0),
arrow(-5,0.30,3,0.30),
arrow(-5,0.15,3,0.15),
arrow(-5,-0.15,3,-0.15),
arrow(-5,-0.30,3,-0.30),

circle(-5,0,0.3),
circle(-5,0,0.3),
circle(-5,0,0.3),
circle(-5,0,0.3-0.02),


arrow(-14,0,-18,0),
arrow(-14,0.30,-18,0.30),
arrow(-14,0.15,-18,0.15),
arrow(-14,-0.15,-18,-0.15),
arrow(-14,-0.30,-18,-0.30),




circle(-14,0,0.3),
circle(-14,0,0.3),
circle(-14,0,0.3),
circle(-14,0,0.3-0.02)
)}}}