<PRE><B>Question 162839</B>
{{{-4&lt;=3x+1&lt;7}}} Start with the given compound inequality.



{{{-4-1&lt;=3x&lt;7-1}}} Subtract {{{1}}} from &lt;b&gt;all&lt;/b&gt; sides.



{{{-5&lt;=3x&lt;7-1}}} Combine like terms on the left side.



{{{-5&lt;=3x&lt;6}}} Combine like terms on the right side.



{{{(-5)/3&lt;=x&lt;(6)/3}}} Divide &lt;b&gt;all&lt;/b&gt; sides by 3 to isolate &quot;x&quot;.



{{{-5/3&lt;=x&lt;2}}} Reduce.



So the answer is {{{-5/3&lt;=x&lt;2}}}




So the answer in interval notation is   &lt;font size=&quot;8&quot;&gt;[&lt;/font&gt;*[Tex \LARGE \bf{-\frac{5}{3},2}]&lt;font size=&quot;8&quot;&gt;)&lt;/font&gt;



Note: remember, brackets &lt;b&gt;in&lt;/b&gt;clude the endpoints while parenthesis &lt;b&gt;ex&lt;/b&gt;clude the endpoints.



Also the answer in set-builder notation is  *[Tex \LARGE \left\{x\|-\frac{5}{3} \le x &lt; 2\right\}]



Here&#39;s the graph of the solution set


{{{drawing(500,80,-10, 7,-10, 10,
number_line( 500, -10, 7 ,-5/3),

blue(line(-5/3,0,2,0)),
blue(line(-5/3,0.30,2,0.30)),
blue(line(-5/3,0.15,2,0.15)),
blue(line(-5/3,-0.15,2,-0.15)),
blue(line(-5/3,-0.30,2,-0.30)),
circle(2,0,0.25),
circle(2,0,0.20)

)}}} Graph of the solution set


Note:

There is a &lt;b&gt;closed&lt;/b&gt; circle at {{{x=-5/3}}} which means that we&#39;re &lt;b&gt;in&lt;/b&gt;cluding this value in the solution set

Also, there is an &lt;b&gt;open&lt;/b&gt; circle at {{{x=2}}} which means that we&#39;re &lt;b&gt;ex&lt;/b&gt;cluding this value from the solution set.
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