Question 221037
# 1


{{{0.9x+6<=1.3x-3}}} Start with the given inequality.



{{{10(0.9x+6)<=10(1.3x-3)}}} Multiply both sides by 10 to clear out the decimals.



{{{9x+60<=13x-30}}} Distribute and multiply.



{{{9x<=13x-30-60}}} Subtract {{{60}}} from both sides.



{{{9x-13x<=-30-60}}} Subtract {{{13x}}} from both sides.



{{{-4x<=-30-60}}} Combine like terms on the left side.



{{{-4x<=-90}}} Combine like terms on the right side.



{{{x>=(-90)/(-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>=45/2}}} Reduce.



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Answer:


So the solution is {{{x>=45/2}}} 



Which in decimal form is {{{x>=22.5}}} 



So the answer in interval notation is   <font size="8">[</font>*[Tex \LARGE \frac{45}{2},\infty]<font size="8">)</font>



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|x\ge\frac{45}{2}\right\}]


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# 2


{{{-3<=3x-2<=-1}}} Start with the given compound inequality.



{{{-3+2<=3x<=-1+2}}} Add {{{2}}} to all sides.



{{{-1<=3x<=-1+2}}} Combine like terms on the left side.



{{{-1<=3x<=1}}} Combine like terms on the right side.



{{{-1/3<=x<=1/3}}} Divide all sides by 3.



So the solution is {{{-1/3<=x<=1/3}}}



So the answer in interval notation is   <font size="8">[</font>*[Tex \LARGE \bf{-\frac{1}{3},\frac{1}{3}}]<font size="8">]</font>



Also, the answer in set-builder notation is  *[Tex \LARGE \left\{x\|-\frac{1}{3} \le x \le \frac{1}{3}\right\}]