SolvingRadicalInequalitiesandGraphingRadicalInequalities
PartI:GraphingInequalities
GraphingLinearInequalities
Step1:Graphthe___________________,whichistheequationoftheline.
Step2:Bylookingatour________________________,determinehowtodrawtheline.
>or<willgiveusa_____________________line.
or willgiveusa_________________line.
Step3:Determinewhichsideoftheboundaryto__________________inordertorepresent
our__________________________________.
Howdoweknowwhichsideoftheboundarytoshade?
Step1:Wemustpickanorderedpairto_____________________.
Step2:Wemust_______________________theorderedpairintoourinequalitytodetermineifitmakesa
_________________statementora___________________statement.
Step3:Ifourstatementistruewewillshade_____________________thepoint.Ifourstatementisfalsewewillshade
____________________thepoint.
Example1:Graphtheinequality.
y> −3x + 2
Nametwopossiblesolutionsforthesystem.
GuidedPractice
Graphandshadethefollowinginequalities.Name2possiblesolutionsforeachsystem.
1.! ≤ 3x + 4
2.! > 2x-1
3.! > 4x-2 4.2" + 2$ > 12 (solvefory)
SolvingSystemsofInequalities
Wehavelearnedthatthesolutionofalinearsystemofequationsoccurswherethetwolines
_______________________________.Likewise,thesolutionofsystemoflinearinequalitiesoccurswherethetworegions
_________________________.Anyorderedpairthatliesinthe_______________________________isasolution.
StepstoSolvingSystemsofInequalities
Step1:Putallinequalitiesin______________________form.
Step2:Graphthe_______________________.
Step3:Shadethe____________________foreachinequality.(Usedifferentcolorsforeach.Darkentheregionwhere
coloroverlaps.)TheoverlapofthetworegionsisyourSOLUTION!
Example1.Solvethesystemofinequalities.
! ≤ 3$ − 6
! > -4$ + 2
Example2:Solvethesystemofinequalities.
!-2$ < 6
$ ≤ -4! + 2 IndependentPractice
Solveeachlinearsystemofinequalitiesbygraphing.Makesuretoshowyourregionofsolutionandidentifyatleasttwo
solutionstothesystem.
! ≤ −2% + 4
1. Solve
% > −3
! ≤ 2$ % − 3
)*
2. Solve
! > $−3
%
#
$
! ≤ %-1
3. Solve
4. Solve
%>
)
%
#
+1
! ≤ 3$ − 2
$ >2 $+1−3