Question 148483


{{{-20 <= 4x -3 <= -2}}} Start with the given compound inequality.



{{{-20+3<=4x<=-2+3}}} Add {{{3}}} to all sides.



{{{-17<=4x<=-2+3}}} Combine like terms on the left side.



{{{-17<=4x<=1}}} Combine like terms on the right side.



{{{(-17)/4<=x<=(1)/4}}} Divide all sides by 4.




So our answer is {{{-17/4<=x<=1/4}}}



So the solution set is  *[Tex \LARGE \left\{x\|-\frac{17}{4} \le x \le \frac{1}{4}\right\}]




And the answer in interval notation is   <font size="8">[</font>*[Tex \LARGE \bf{-\frac{17}{4},\frac{1}{4}}]<font size="8">]</font>



Here's the graph of the solution set


{{{drawing(500,80,-22, 6,-10, 10,
number_line( 500, -22, 6 ,-17/4,1/4),

blue(line(-17/4,0,1/4,0)),
blue(line(-17/4,0.30,1/4,0.30)),
blue(line(-17/4,0.15,1/4,0.15)),
blue(line(-17/4,-0.15,1/4,-0.15)),
blue(line(-17/4,-0.30,1/4,-0.30))

)}}} Graph of the solution set


Note:

There is a <b>closed</b> circle at {{{x=-17/4}}} which means that we're including this value in the solution set

Also, there is a <b>closed</b> circle at {{{x=1/4}}} which means that we're including this value in the solution set.

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<pre>
1[-83 - (54 - 87)]=1[-83 - (-33)]
                  =1[-83 +33]
                  =1[-50]
                  =-50

</pre>