SOLUTION: Appreciate any assistance in solving the following absolute value equations: 1. |3-3/4x|=1/4 2. 1/3|2x-1|<1 3. 3-1/2|1/2x-4|=2

Algebra ->  Absolute-value -> SOLUTION: Appreciate any assistance in solving the following absolute value equations: 1. |3-3/4x|=1/4 2. 1/3|2x-1|<1 3. 3-1/2|1/2x-4|=2      Log On


   

Question 66614: Appreciate any assistance in solving the following absolute value equations:
1. |3-3/4x|=1/4
2. 1/3|2x-1|<1
3. 3-1/2|1/2x-4|=2
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Appreciate any assistance in solving the following absolute value equations:
1. |3-3/4x|=1/4
abs%283-%283%2F4%29x%29=1%2F4
3-%283%2F4%29x=1%2F4 or 3-%283%2F4%29x=-1%2F4
3-3-%283%2F4%29x=1%2F4-3 or 3-3-%283%2F4%29x=-1%2F4-3
-%283%2F4%29x=1%2F4-12%2F4 or -%283%2F4%29x=-1%2F4-12%2F4
-%283%2F4%29x=-11%2F4 or -%283%2F4%29x=-13%2F4
%28-4%2F3%29%28-3%2F4%29x=%28-4%2F3%29%28-11%2F4%29 or %28-4%2F3%29%28-3%2F4%29x=%28-4%2F3%29%28-13%2F4%29
highlight%28x=11%2F3%29 or x=13%2F3
:
2. 1/3|2x-1|<1
%281%2F3%29%2Aabs%282x-1%29%3C1
3%281%2F3%29%2Aabs%282x-1%29%3C3%281%29
abs%282x-1%29%3C3
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%3C2x-1%3C3
-3%2B1%3C2x-1%2B1%3C3%2B1
-2%3C2x%3C4
-2%2F2%3C2x%2F2%3C4%2F2
highlight%28-1%3Cx%3C2%29
3. 3-1/2|1/2x-4|=2
3-%281%2F2%29%2Aabs%28%281%2F2%29x-4%29=2
3-3-%281%2F2%29%2Aabs%28%281%2F2%29x-4%29=2-3
%28-1%2F2%29%2Aabs%28%281%2F2%29x-4%29=-1
-2%28-1%2F2%29%2Aabs%28%281%2F2%29x-4%29=-2%28-1%29
abs%28%281%2F2%29x-4%29=2
%281%2F2%29x-4=2 or %281%2F2%29x-4=-2
%281%2F2%29x-4%2B4=2%2B4 or %281%2F2%29x-4%2B4=-2%2B4
%281%2F2%29x=6 or %281%2F2%29x=2
2%281%2F2%29x=2%286%29 or 2%281%2F2%29x=2%282%29
highlight%28x=12%29 or highlight%28x=4%29
Happy Calculating!!!!