Question 395822


{{{-5(x-4)+3x>-16}}} Start with the given inequality.



{{{-5x+20+3x>-16}}} Distribute.



{{{-2x+20>-16}}} Combine like terms on the left side.



{{{-2x>-16-20}}} Subtract {{{20}}} from both sides.



{{{-2x>-36}}} Combine like terms on the right side.



{{{x<(-36)/(-2)}}} Divide both sides by {{{-2}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<18}}} Reduce.



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Answer:


So the solution is {{{x<18}}} 



So the answer in interval notation is *[Tex \LARGE \left(-\infty,18\right)]



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x<18\right\}]



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


{{{drawing(500,80,8, 28,-10, 10,
number_line( 500, 8, 28),


arrow(18,0,8,0),
arrow(18,0.30,8,0.30),
arrow(18,0.15,8,0.15),
arrow(18,-0.15,8,-0.15),
arrow(18,-0.30,8,-0.30),




circle(18,0,0.3),
circle(18,0,0.3),
circle(18,0,0.3),
circle(18,0,0.3-0.02)
)}}}


Note: there is an open circle at the endpoint



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Jim