Question 143691
{{{5>-2x+4}}} Start with the first inequality



{{{0>-2x+4-5}}}Subtract 5 from both sides



{{{+2x>4-5}}} Add 2x to both sides



{{{2x+0>-1}}} Combine like terms on the right side



{{{x>(-1)/(2)}}} Divide both sides by 2 to isolate x 




{{{x>-1/2}}} Reduce



So our answer is {{{x>-1/2}}} which looks like *[Tex \LARGE \left(-\frac{1}{2},\infty\right)] in interval notation




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{{{11<=-5x+4}}} Now move onto the second inequality



{{{0<=-5x+4-11}}}Subtract 11 from both sides



{{{+5x<=4-11}}} Add 5x to both sides



{{{5x+0<=-7}}} Combine like terms on the right side



{{{x<=(-7)/(5)}}} Divide both sides by 5 to isolate x 




{{{x<=-7/5}}} Reduce



So our answer is {{{x<=-7/5}}} which looks like <font size="8">(</font>*[Tex \LARGE \bf{-\infty,-\frac{7}{5}}]<font size="8">]</font> in interval notation. 





Now combine the two solutions sets to get 



<font size="8">(</font>*[Tex \LARGE \bf{-\infty,-\frac{7}{5}}]<font size="8">]</font>*[Tex \LARGE \cup] *[Tex \LARGE \left(-\frac{1}{2},\infty\right)]


note: the "sideways 8" is the infinity symbol.



So the answer is choice c)