Question 348009

{{{abs(x+8)>=7}}} Start with the given inequality



Break up the absolute value (remember, if you have {{{abs(x)>= a}}}, then {{{x <= -a}}} or {{{x >= a}}})


{{{x+8 <= -7}}} or {{{x+8 >= 7}}} Break up the absolute value inequality using the given rule





Now lets focus on the first inequality  {{{x+8 <= -7}}}



{{{x+8<=-7}}} Start with the given inequality



{{{x<=-7-8}}}Subtract 8 from both sides



{{{x<=-15}}} Combine like terms on the right side



Now lets focus on the second inequality  {{{x+8 >= 7}}}



{{{x+8>=7}}} Start with the given inequality



{{{x>=7-8}}}Subtract 8 from both sides



{{{x>=-1}}} Combine like terms on the right side




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


Answer:


So our answer is


{{{x <= -15}}} or {{{x >= -1}}}



which looks like this in interval notation



*[Tex \LARGE \left(-\infty,-15\right)\cup\left(-1,\infty\right)]



if you wanted to graph the solution set, you would get


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -18, 2),

blue(arrow(-7.5,-7,-10,-7)),
blue(arrow(-7.5,-6.5,-10,-6.5)),
blue(arrow(-7.5,-6,-10,-6)),
blue(arrow(-7.5,-5.5,-10,-5.5)),
blue(arrow(-7.5,-5,-10,-5)),
blue(arrow(7.5,-7,10,-7)),
blue(arrow(7.5,-6.5,10,-6.5)),
blue(arrow(7.5,-6,10,-6)),
blue(arrow(7.5,-5.5,10,-5.5)),
blue(arrow(7.5,-5,10,-5)),

circle(-7,-5.8,0.35),
circle(-7,-5.8,0.4),
circle(-7,-5.8,0.45),


circle(7,-5.8,0.35),
circle(7,-5.8,0.4),
circle(7,-5.8,0.45)




)}}} Graph of the solution set in blue and the excluded values represented by open circles



If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=Algebra%20Help">jim_thompson5910@hotmail.com</a>


Also, feel free to check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">tutoring website</a>


Jim