Question 150976

{{{5x+5<3(x+2)}}} Start with the given inequality.



{{{5x+5<3x+6}}} Distribute.



{{{5x<3x+6-5}}} Subtract {{{5}}} from both sides.



{{{5x-3x<6-5}}} Subtract {{{3x}}} from both sides.



{{{2x<6-5}}} Combine like terms on the left side.



{{{2x<1}}} Combine like terms on the right side.



{{{x<(1)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}. 



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Answer:


So the answer is {{{x<1/2}}} 



Which approximates to {{{x<0.5}}}





So the answer in interval notation is *[Tex \LARGE \left(-\infty,\frac{1}{2}\right)]





Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x<\frac{1}{2}\right\}]




Here's the graph of the solution set


{{{drawing(500,80,-9, 11,-10, 10,
number_line( 500, -9, 11),


arrow(1/2,0,-9,0),
arrow(1/2,0.30,-9,0.30),
arrow(1/2,0.15,-9,0.15),
arrow(1/2,-0.15,-9,-0.15),
arrow(1/2,-0.30,-9,-0.30),




circle(1/2,0,0.3),
circle(1/2,0,0.3),
circle(1/2,0,0.3),
circle(1/2,0,0.3-0.02)
)}}}