Question 177272
{{{4x+3<=9}}} Start with the given inequality.



{{{4x<=9-3}}} Subtract {{{3}}} from both sides.



{{{4x<=6}}} Combine like terms on the right side.



{{{x<=(6)/(4)}}} Divide both sides by {{{4}}} to isolate {{{x}}}. 



{{{x<=3/2}}} Reduce.



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Answer:


So the answer is {{{x<=3/2}}} 



So the answer in interval notation is   <font size="8">(</font>*[Tex \LARGE \bf{-\infty,\frac{3}{2}}]<font size="8">]</font>




Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x\le\frac{3}{2}\right\}]



Here's the graph of the solution set


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


arrow(3/2,0,-7,0),
arrow(3/2,0.30,-7,0.30),
arrow(3/2,0.15,-7,0.15),
arrow(3/2,-0.15,-7,-0.15),
arrow(3/2,-0.30,-7,-0.30),




circle(3/2,0,0.2),
circle(3/2,0,0.15),
circle(3/2,0,0.1),
circle(3/2,0,0.2-0.02)
)}}}


Note: the endpoint at {{{x=3/2}}} is a closed circle