Question 712154
{{{2(x+5)+1>5+3x}}} Start with the given inequality.



{{{2x+10+1>5+3x}}} Distribute.



{{{2x+11>5+3x}}} Combine like terms on the left side.



{{{2x>5+3x-11}}} Subtract {{{11}}} from both sides.



{{{2x-3x>5-11}}} Subtract {{{3x}}} from both sides.



{{{-x>5-11}}} Combine like terms on the left side.



{{{-x>-6}}} Combine like terms on the right side.



{{{x<(-6)/(-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<6}}} Reduce.



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Answer:


So the solution is {{{x<6}}} 



The answer in interval notation is *[Tex \LARGE \left(-\infty,6\right)]




To graph the inequality {{{x<6}}}, draw out a number line.


Then plot an open circle at 6.


Then shade to the left of the open circle.


The graph will look something like this




{{{drawing(500,80,-4, 16,-10, 10,
number_line( 500, -4, 16),


arrow(6,0,-4,0),
arrow(6,0.30,-4,0.30),
arrow(6,0.15,-4,0.15),
arrow(6,-0.15,-4,-0.15),
arrow(6,-0.30,-4,-0.30),




circle(6,0,0.3),
circle(6,0,0.3),
circle(6,0,0.3),
circle(6,0,0.3-0.02)
)}}}