Question 115214
{{{(1/5)x<35}}} Start with the given inequality




{{{(5)((1/5)x)<(5)(35)}}} Multiply both sides by 5


{{{x<175}}} Multiply



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Answer:

So our answer is {{{x<175}}} 


Now let's graph the solution


Start with the given inequality:


{{{x<175}}}


Set up a number line:

{{{number_line(500,165,185)}}} 


Now plot the point {{{x=175}}} on the number line



{{{number_line(500,165,185, 175)}}}



Now pick any test point you want, I'm going to choose x=0, and test the inequality {{{x<175}}}



{{{0<175}}} 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=175}}} as the boundary.This means we shade everything to the left of the point {{{x=175}}} like this:

{{{drawing(500,50,165,185,-10,10,
number_line(500,165,185),
circle(175,-5.8,0.35),
circle(175,-5.8,0.4),
circle(175,-5.8,0.45),
blue(line(175,-5,175-10,-5)),
blue(line(175,-6,175-10,-6)),
blue(line(175,-7,175-10,-7)),
blue(arrow(175,-5,175-10.2,-5)),
blue(arrow(175,-5.5,175-10.2,-5.5)),
blue(arrow(175,-6,175-10.2,-6))
)}}}  Graph of {{{x<175}}} with the shaded region in blue


note: at the point {{{x=175}}}, there is an <font size=4><b>open</b></font> circle. This means the point {{{x=175}}} is excluded from the solution set.