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Solve 2 < |x + 7| < 5.

 Jun 4, 2020
 #1
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x = -4, -3

 Jun 4, 2020
 #2
avatar+1130 
+22

\(x= \text{any number between -3 and -5.000...02 exclusively }\)because -2.00...01 is the biggest and -4.99999 is the smallest number since when they add 7 they are a number between 2 and 5 so it because any one of the numbers like -2.999... and -5.00...01... would add up to 2.00...01 and 4.999...

 Jun 4, 2020
 #3
avatar+26735 
+1

x+7 <5    yields    x < -2

x+7>-5   yields     x > -12

 

 

x+7>2   yields   x > -5

x+7 <-2 yields   x < -9

 

combining     ( -12,-9) U ( -5,-2)

 Jun 4, 2020

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