SOLUTION: Hello I'm in Algebra II/Trig and we are reviewing absolute value equations, I forgot how to do these and I need help. Thanks for taking your time for this: 1/7|4z+5|+2>5 I wo

Algebra ->  Absolute-value -> SOLUTION: Hello I'm in Algebra II/Trig and we are reviewing absolute value equations, I forgot how to do these and I need help. Thanks for taking your time for this: 1/7|4z+5|+2>5 I wo      Log On


   



Question 898344: Hello I'm in Algebra II/Trig and we are reviewing absolute value equations, I forgot how to do these and I need help. Thanks for taking your time for this:
1/7|4z+5|+2>5
I worked on some of the question but I am not sure if it is correct:
1/7+4z+7>5
(7/1)1/7+4z>-2(7/1)
4z>-14
z=-7/2

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Part of your inequality as given is unclear. I will assume you intend the fraction as a separate factor: %281%2F7%29abs%284z%2B5%29%2B2%3E5

Simplify up to the absolute value function.
abs%284z%2B5%29%3E%285-2%29%2A7
abs%284z%2B5%29%3E21

Now solve for each of two different cases.

4z+5 may be positive or negative or zero.

highlight_green%284z%2B5%3E=0%29:
4z%2B5%3E21
4z%3E16
z%3E16%2F4
z%3E4

highlight_green%284z%2B5%3C0%29:
-4z-5%3E21
-4z%3E21%2B5
-4z%3E26
CAREFUL HERE....
z%3C26%2F%28-4%29
z%3C-13%2F2

Put together, the solution for z is
highlight%28z%3C-13%2F2%29 OR highlight%28z%3E4%29