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How many integers satisfy the inequality \((x+3)^{2}\leq1\)?

 

thanks in advance

 Jul 27, 2019
 #1
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+1

(x + 3)^2 <=1
x^2 + 6 x + 9<=1
-4<=x<=-2
x = -2, and x = -3 and x = - 4

 Jul 27, 2019
 #2
avatar+8725 
+3

If    (x + 3)2  ≤  1    then the absolute value of   x + 3   must be less than  1

 

| x + 3 |  ≤  1

 

Then in order for that to be true, it must be that

 

-1  ≤  x + 3  ≤  1

 

Subtract  3  from all parts of the inequality.

 

-4  ≤  x  ≤  -2

 

Then the integer solutions to that inequality are clearly

 

x = -4,  x = -3,  x = -2

 Jul 27, 2019
 #3
avatar+1040 
+1

Thanks guest and hectictar!!

 Jul 28, 2019

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