Question 198337
{{{-x-6>-3x+9}}} Start with the given inequality.



{{{-x>-3x+9+6}}} Add {{{6}}} to both sides.



{{{-x+3x>9+6}}} Add {{{3x}}} to both sides.



{{{2x>9+6}}} Combine like terms on the left side.



{{{2x>15}}} Combine like terms on the right side.



{{{x>(15)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}. 



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Answer:


So the answer is {{{x>15/2}}} 



Which approximates to {{{x>7.5}}}




So the answer in interval notation is *[Tex \LARGE \left(\frac{15}{2},\infty\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x>\frac{15}{2}\right\}]



Here's the graph of the solution set


{{{drawing(500,80,5, 25,-10, 10,
number_line( 500, 5, 25),

arrow(15/2,0,25,0),
arrow(15/2,0.30,25,0.30),
arrow(15/2,0.15,25,0.15),
arrow(15/2,-0.15,25,-0.15),
arrow(15/2,-0.30,25,-0.30),

circle(15/2,0,0.3),
circle(15/2,0,0.3),
circle(15/2,0,0.3),
circle(15/2,0,0.3-0.02)
)}}}