SOLUTION: -(3*7 < = -4 power 2 -8(x-2)+7x < = -(12*3) _______ ___________ ___________ ___________ 14/2 ) (2/3x + 17y)power 0 +5

Algebra ->  Inequalities -> SOLUTION: -(3*7 < = -4 power 2 -8(x-2)+7x < = -(12*3) _______ ___________ ___________ ___________ 14/2 ) (2/3x + 17y)power 0 +5       Log On


   

Question 173123: -(3*7 < = -4 power 2 -8(x-2)+7x < = -(12*3)
_______ _______________________ ___________
14/2 ) (2/3x + 17y)power 0 +5 -3 power 2
solve for x
this is extra credit but I got 50>= x >= 56 which can't be correct?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the inequality is



First, note that ANY number (except 0) to the zeroth power is 1. So this means that %28%282%2F3%29x+%2B+17y%29%5E0=1


Also, -3*7=-21 and 14%2F2=7. So the left side goes from %0D%0A-%283%2A7%29%2F%2814%2F2%29 to -21%2F7 which reduces to -3


Also, -12*3=-36 and -3%5E2=-9. So the right side goes from -%2812%2A3%29%2F%28-3%5E2%29 to -36%2F%28-9%29 which reduces to 4


So the inequality





simplifies to



-3%3C=%28-4%5E2-8%28x-2%29%2B7x%29%2F%281%2B5%29%3C=4



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-3%3C=%28-4%5E2-8%28x-2%29%2B7x%29%2F%281%2B5%29%3C=4 Start with the given compound inequality


-3%3C=%28-16-8%28x-2%29%2B7x%29%2F%281%2B5%29%3C=4 Square 4 to get 16


-3%3C=%28-16-8x%2B16%2B7x%29%2F%281%2B5%29%3C=4 Distribute


-3%3C=%28-x%29%2F%286%29%3C=4 Combine like terms.


-18%3C=-x%3C=24 Multiply ALL sides by 6


18%3E=-x%3E=-24 Divide ALL sides by -1 to isolate "x" (this will flip the signs)



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Answer:


So the solution is -24%3C=x%3C=18




So the answer in interval notation is []


Also, the answer in set-builder notation is


Here's the graph of the solution set on a number line:

Graph of the solution set

Note:
There is a closed circle at x=-24 which means that we're including this value in the solution set
Also, there is a closed circle at x=18 which means that we're including this value in the solution set.