Question 158280

{{{3.5x+23.6>59.0-8.3x}}} Start with the given inequality.



{{{10(3.5x+23.6)>10(59.0-8.3x)}}} Multiply both sides by 10 to clear out the decimals.



{{{35x+236>590-83x}}} Distribute and multiply.



{{{35x>590-83x-236}}} Subtract {{{236}}} from both sides.



{{{35x+83x>590-236}}} Add {{{83x}}} to both sides.



{{{118x>590-236}}} Combine like terms on the left side.



{{{118x>354}}} Combine like terms on the right side.



{{{x>(354)/(118)}}} Divide both sides by {{{118}}} to isolate {{{x}}}. 



{{{x>3}}} Reduce.



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Answer:


So the answer is {{{x>3}}}




So the answer in interval notation is *[Tex \LARGE \left(3,\infty\right)]



Also the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x>3\right\}]




Here's the graph of the solution set


{{{drawing(500,80,-7, 13,-10, 10,
number_line( 500, -7, 13),

arrow(3,0,13,0),
arrow(3,0.30,13,0.30),
arrow(3,0.15,13,0.15),
arrow(3,-0.15,13,-0.15),
arrow(3,-0.30,13,-0.30),

circle(3,0,0.3),
circle(3,0,0.3),
circle(3,0,0.3),
circle(3,0,0.3-0.02)
)}}}