SOLUTION: I have tried these problems a few times and cannot come up with a solution...help! a) 3|x|+12=7 b) 5|x+3| +6=3 c) 12-|2x+7>=14

Algebra ->  Algebra  -> Absolute-value -> SOLUTION: I have tried these problems a few times and cannot come up with a solution...help! a) 3|x|+12=7 b) 5|x+3| +6=3 c) 12-|2x+7>=14      Log On

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Question 211558: I have tried these problems a few times and cannot come up with a solution...help!
a) 3|x|+12=7
b) 5|x+3| +6=3
c) 12-|2x+7>=14
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
a)

3%2Aabs%28x%29%2B12=7 Start with the given equation


3%2Aabs%28x%29=-5 Subtract 12 from both sides.


abs%28x%29=-5%2F3 Divide both sides by 3



Since the expression abs%28x%29=-5%2F3 is never true (note: remember, the absolute value of any number is always positive), there are no solutions to abs%28x%29=-5%2F3


So there are no solutions.



b)


5%2Aabs%28x%2B3%29%2B6=3 Start with the given equation


5%2Aabs%28x%2B3%29=-3 Subtract 6 from both sides.


abs%28x%2B3%29=-3%2F5 Divide both sides by 5



Since the expression abs%28x%2B3%29=-0.6 is never true (note: remember, the absolute value of any number is always positive), there are no solutions to abs%28x%2B3%29=-0.6


So there are no solutions.


c)

12-abs%282x%2B7%29%3E=14 Start with the given inequality.


-abs%282x%2B7%29%3E=14-12 Subtract 12 from both sides.


-abs%282x%2B7%29%3E=2 Combine like terms.


abs%282x%2B7%29%3C=-2 Multiply both sides by -1 (this will flip the inequality).


Because abs%282x%2B7%29%3E=0 for ALL 'x', this means that abs%282x%2B7%29%3C=-2 is simply not possible.

So there are no solutions.



So this might explain why you couldn't come up with a solution....as there are none. However, make sure that you copied down the problems correctly.