Question 201220
{{{-8x-2>=-7x-12}}} Start with the given inequality.



{{{-8x>=-7x-12+2}}} Add {{{2}}} to both sides.



{{{-8x+7x>=-12+2}}} Add {{{7x}}} to both sides.



{{{-x>=-12+2}}} Combine like terms on the left side.



{{{-x>=-10}}} Combine like terms on the right side.



{{{x<=(-10)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<=10}}} Reduce.



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Answer:


So the solution is {{{x<=10}}}




So the answer in interval notation is   <font size="8">(</font>*[Tex \LARGE \bf{-\infty,10}]<font size="8">]</font>




Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x\le10\right\}]



Here's the graph of the solution set on a number line:


{{{drawing(500,80,0, 20,-10, 10,
number_line( 500, 0, 20),


arrow(10,0,0,0),
arrow(10,0.30,0,0.30),
arrow(10,0.15,0,0.15),
arrow(10,-0.15,0,-0.15),
arrow(10,-0.30,0,-0.30),




circle(10,0,0.2),
circle(10,0,0.15),
circle(10,0,0.1),
circle(10,0,0.2-0.02)
)}}}


Note: there is a CLOSED circle at the endpoint.