Question 187311
{{{-x/2+4<3x/2+8}}} Start with the given inequality.



{{{cross(2)(-x/cross(2))+2(4)<cross(2)(3x/cross(2))+2(8)}}} Multiply EVERY term  by the LCD {{{2}}} to clear the fractions.



{{{-x+8<3x+16}}} Distribute and multiply.



{{{-x<3x+16-8}}} Subtract {{{8}}} from both sides.



{{{-x-3x<16-8}}} Subtract {{{3x}}} from both sides.



{{{-4x<16-8}}} Combine like terms on the left side.



{{{-4x<8}}} Combine like terms on the right side.



{{{x>(8)/(-4)}}} Divide both sides by {{{-4}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x>-2}}} Reduce.



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Answer:


So the answer is {{{x>-2}}} 




The answer in interval notation is *[Tex \LARGE \left(-2,\infty\right)]



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



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


{{{drawing(500,80,-12, 8,-10, 10,
number_line( 500, -12, 8),

arrow(-2,0,8,0),
arrow(-2,0.30,8,0.30),
arrow(-2,0.15,8,0.15),
arrow(-2,-0.15,8,-0.15),
arrow(-2,-0.30,8,-0.30),

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