SOLUTION: i need help on absolute values please. this is what i have tried so far on my problems: (1/2)|2w-1|-3>1 i added 3 to the 1 to get 4 then i multiplied one have by its reciprocal to

Algebra ->  Absolute-value -> SOLUTION: i need help on absolute values please. this is what i have tried so far on my problems: (1/2)|2w-1|-3>1 i added 3 to the 1 to get 4 then i multiplied one have by its reciprocal to      Log On


   

Question 805756: i need help on absolute values please. this is what i have tried so far on my problems: (1/2)|2w-1|-3>1
i added 3 to the 1 to get 4 then i multiplied one have by its reciprocal to its self and 4 to get 8. i added one to the 8 to get 9 divided by two.
The second problem is : (3/4)|8t-12|=6(t-1) i didn't know what to do on this one but i did try the first one.

Found 2 solutions by mananth, josgarithmetic:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(1/2)|2w-1|-3>1
(1/2)|2w-1|>1+3
multiply by 2
|2w-1| >4*2
|2w-1|>8
-8<(2w-1)>8
add1
-7<2w>9
/2
%28-7%2F2%29%3C+w+%3E%289%2F2%29

Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
(1/2)|2w-1|-3>1
%281%2F2%29%2Aabs%282w-1%29-3%3E1

Handle the absolute value function as a variable. Solve for it:

abs%282w-1%29%3E2%281%2B3%29
abs%282w-1%29%3E8

Solve based on each of the two conditions:

The argument is positive or zero, 2w-1%3E=0.
2w-1%3E8
2w%3E8%2B1
2w%3E9
w%3E9%2F2

The argument may be negative, 2w-1%3C0.
abs%282w-1%29=-%282w-1%29=1-2w.
1-2w%3E8
-2w%3E8%2B1
-2w%3E9
Next step requires care;
-2w%28-1%2F2%29%3C9%2A%28-1%2F2%29
w%3C-9%2F2

Combine the two results to complete the answer.
highlight%28w%3C-9%2F2%29 OR highlight%28w%3E9%2F2%29.