Question 164981
Solve the following absolute value inequality: I am not quit sure how to do this problem with a fraction. Thank you 
<pre><font size = 4 color="indigo"><b>
{{{1/2}}}{{{abs(x-2)<4}}}

Multiply both sides by {{{2}}}

{{{2*(1/2)}}}{{{abs(x-2)<2*4}}}

{{{cross(2)*(1/cross(2))}}}{{{abs(x-2)<2*4}}}

{{{abs(x-2)<8}}}

RULES for removing absolute value bars in inequalities.
(Assume A is a non-negative number)

1. {{{abs(EXPRESSION)<A}}} becomes {{{-A<EXPRESSION<A}}}
2. {{{abs(EXPRESSION)<=A}}} becomes {{{-A<=EXPRESSION<=A}}}
3. {{{abs(EXPRESSION)>A}}} becomes {{{matrix(1,3,EXPRESSION<-A, OR, EXPRESSION>A)}}}
4. {{{abs(EXPRESSION)>=A}}} becomes {{{matrix(1,3,EXPRESSION<=-A, OR, EXPRESSION>=A)}}}

Your problem is case 1

{{{abs(x-2)<8}}} becomes {{{-8<x-2<8}}}

Solve for x in the middle

{{{-8<x-2<8}}}

Add 2 to all three sides:

{{{-8+2<x-2+2<8+2}}}

{{{-6<x<10}}}

In interval notation:

(-6, 10)

Edwin</pre>