Question 118102


{{{5x-4<6x+2}}} Start with the given inequality




{{{5x<6x+2+4}}}Add 4 to both sides



{{{5x-6x<2+4}}} Subtract 6x from both sides



{{{-x<2+4}}} Combine like terms on the left side



{{{-x<6}}} Combine like terms on the right side



{{{x>(6)/(-1)}}} Divide both sides by -1 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) 




{{{x>-6}}} Divide


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Answer:

So our answer is {{{x>-6}}} 




Now let's graph the solution set



Start with the given inequality:


{{{x>-6}}}


Set up a number line:

{{{number_line(500,-16,4)}}} 


Now plot the point {{{x=-6}}} on the number line



{{{number_line(500,-16,4, -6)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x>-6}}}



{{{0>-6}}} Plug in {{{x=0}}}



Since this inequality is true, we simply shade the entire portion in which contains the point x=0 using the point {{{x=-6}}} as the boundary.This means we shade everything to the right of the point {{{x=-6}}} like this:

{{{drawing(500,50,-16,4,-10,10,
number_line(500,-16,4),
circle(-6,-5.8,0.35),
circle(-6,-5.8,0.4),
circle(-6,-5.8,0.45),
blue(line(-6,-5,-6+10,-5)),
blue(line(-6,-6,-6+10,-6)),
blue(line(-6,-7,-6+10,-7)),
blue(arrow(-6,-5,-6+10.2,-5)),
blue(arrow(-6,-5.5,-6+10.2,-5.5)),
blue(arrow(-6,-6,-6+10.2,-6))
)}}}  Graph of {{{x>-6}}} with the shaded region in blue

note: at the point {{{x=-6}}}, there is an <font size=4><b>open</b></font> circle. This means the point {{{x=-6}}} is excluded from the solution set.