Question 59636
 Solve the following
: 
a)            |2x-9|<3  
{{{-3<2x-9<3}}}
{{{-3+9<2x-9+9<3+9}}}
{{{6<2x<12}}}
{{{6/2<2x/2<12/2}}}
{{{3<x<6}}}                      

b)            |3x-4|<-13  
No solution |x| cannot be less than 0.                 
 
c)            |2x-2|=|x+1|  
{{{(2x-2)^2=(x+1)^2}}}  Square both sides
{{{4x^2-8x+4=x^2+2x+1}}}  Set = to 0
{{{4x^2-x^2-8x-2x+4-1=x^2-x^2+2x-2x+1-1}}}
{{{3x^2-10x+3=0}}} Factor
{{{3x^2-9x-x+3=0}}}
{{{3x(x-3)-1(x-3)=0}}}
{{{(3x-1)(x-3)=0}}}
3x-1=0 and x-3=0
3x-1+1=0+1 and x-3+3=0+3
3x=1 and x=3
3x/3=1/3 and x=3
x=1/3 and x=3         
 :
d)            Determine which of the following points are solutions to the system                 
 
               {{{y>-2x+1}}}
               {{{y<3x+5 }}}           (-3, 2), (-1, 5), (3, 6)
For (-3,2)
{{{2>-2(-3)+1}}}
{{{2>6+1}}}
{{{2>7}}}  2 is not greater than 7 (-3,2) is not a solution.
:
For (-1,5)
{{{5>-2(-1)+1}}}
{{{5>2+1}}}
{{{5>3}}}    It's true for the first equation, check the second.
{{{5<3(-1)+5}}}
{{{5<-3+5}}}
{{{5<2}}}  5 is not less than 2 (-1,5) is not a solution of the system.
:
For (3,6)
{{{6>-2(3)+1}}}
{{{6>-6+1}}}
{{{6>-5}}}  It's true for the first equation, check the second.
{{{6<3(3)+5}}}
{{{6<9+5}}}
{{{6<14}}}  It's true for the second also, therefore (3,6) is a solution to the system.
Happy Calculating!!!