Question 66614
Appreciate any assistance in solving the following absolute value equations: 

1.   |3-3/4x|=1/4  
{{{abs(3-(3/4)x)=1/4}}}
{{{3-(3/4)x=1/4}}} or {{{3-(3/4)x=-1/4}}}
{{{3-3-(3/4)x=1/4-3}}} or {{{3-3-(3/4)x=-1/4-3}}}
{{{-(3/4)x=1/4-12/4}}} or {{{-(3/4)x=-1/4-12/4}}}
{{{-(3/4)x=-11/4}}} or {{{-(3/4)x=-13/4}}}
{{{(-4/3)(-3/4)x=(-4/3)(-11/4)}}} or {{{(-4/3)(-3/4)x=(-4/3)(-13/4)}}}
{{{highlight(x=11/3)}}} or {{{x=13/3}}}
:
2.   1/3|2x-1|<1
{{{(1/3)*abs(2x-1)<1}}}
{{{3(1/3)*abs(2x-1)<3(1)}}}
{{{abs(2x-1)<3}}}
Because this is a less than, it's an and situtation, I do these like this.  But you can do what we did with the others and replace the word "or" with "and":
{{{-3<2x-1<3}}}
{{{-3+1<2x-1+1<3+1}}}
{{{-2<2x<4}}}
{{{-2/2<2x/2<4/2}}}
{{{highlight(-1<x<2)}}}
3.   3-1/2|1/2x-4|=2
{{{3-(1/2)*abs((1/2)x-4)=2}}}
{{{3-3-(1/2)*abs((1/2)x-4)=2-3}}}
{{{(-1/2)*abs((1/2)x-4)=-1}}}
{{{-2(-1/2)*abs((1/2)x-4)=-2(-1)}}}
{{{abs((1/2)x-4)=2}}}
{{{(1/2)x-4=2}}} or {{{(1/2)x-4=-2}}}
{{{(1/2)x-4+4=2+4}}} or {{{(1/2)x-4+4=-2+4}}}
{{{(1/2)x=6}}} or {{{(1/2)x=2}}}
{{{2(1/2)x=2(6)}}} or {{{2(1/2)x=2(2)}}}
{{{highlight(x=12)}}} or {{{highlight(x=4)}}}
Happy Calculating!!!!