Question 1203084
<pre>

|x+3| < 1/2 , then |4x+13| < 3

{{{abs(x+3)<1/2}}}
By definition,
{{{-1/2<x+3<1/2}}}
Subtract 3 from all 3 sides
{{{-1/2-3<x+3-3<1/2-3}}}
Simplify
{{{-7/2<x<-5/2}}}
Multiply all 3 sides by 4
{{{-14<4x<-10}}}
Add 13 to all 3 sides
{{{-14+13<4x+13<-10+13}}}
Simplify
{{{-1<4x+13<3}}}
Since -3 < -1
{{{-3<4x+13<3}}}
By definition,
{{{abs(4x+13)<3}}}

Edwin</pre>