SOLUTION: PLEASE HELP ME SOLVE MY TWO QUESTIONS. Thank you so much! |2(p-4)-5|=23 2+4|5x-7|=46

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Question 898942: PLEASE HELP ME SOLVE MY TWO QUESTIONS. Thank you so much!
|2(p-4)-5|=23
2+4|5x-7|=46
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
This is what to do, as an explanation, but not the actual solution steps.

The second equation: Solve for the absolute value as its own variable, and then solve for each of the two cases 5x-7%3E=0 and 5x-7%3C0.

The first equation already equates an absolute value to a positive real number.
Solve for each of the two cases, 2%28p-4%29-5%3E=0 and 2%28p-4%29-5%3C0.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

PLEASE HELP ME SOLVE MY TWO QUESTIONS. Thank you so much!
|2(p-4)-5|=23
2+4|5x-7|=46


abs%282%28p+-+4%29+-+5%29+=+23

abs%282p+-+8+-+5%29+=+23

abs%282p+-+13%29+=+23



Either:

2p - 13 = 23                     OR                   2p - 13 = - 23

     2p = 23 + 13                OR                        2p = - 23 + 13

     2p = 36                     OR                        2p = - 10

      p+=+36%2F2____highlight_green%28p+=+18%29           OR                           p+=+%28-+10%29%2F2_____highlight_green%28p+=+-+5%29



2+%2B+4abs%285x+-+7%29+=+46

4abs%285x+-+7%29+=+46+-+2

4abs%285x+-+7%29+=+44

abs%285x+-+7%29+=+44%2F4

abs%285x+-+7%29+=+11



Either:

5x - 7 = 11                      OR                    5x - 7 = - 11

    5x = 11 + 7                  OR                        5x = - 11 + 7

    5x = 18                      OR                        5x = - 4

     x+=+18%2F5____highlight_green%28x+=+3.6%29           OR                        highlight_green%28x+=+%28-+4%29%2F5%29

You can do the check!! 



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