Question 119858



{{{1<-2x+7<9}}} Start with the given inequality






{{{-6<-2x<2}}} Subtract 7 from all sides







{{{3>x>-1}}} Divide every side by -2 to isolate x. Remember, dividing every side of an inequality by a negative number flips the inequality signs





{{{-1<x<3}}} Rearrange the inequality.



So the solution in interval notation is: (-1,3)



Now let's graph the solution set


{{{drawing(500,50,-10,10,-10,10,
number_line( 500, -9, 11),
blue(line(-1.75,-7,1.85,-7)),
blue(line(-1.75,-6,1.85,-6)),
blue(line(-1.75,-5,1.85,-5)),

circle(-2,-5.8,0.35),
circle(-2,-5.8,0.4),
circle(-2,-5.8,0.45),

circle(2,-5.8,0.35),
circle(2,-5.8,0.4),
circle(2,-5.8,0.45)


)}}}


Note: at {{{x=-1}}} there is a <font size="4"><b>open</b></font>  circle (which means this point is excluded) and at {{{x=3}}} there is a <font size="4"><b>open</b></font> circle (which means this point is excluded)