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

thanks in advance

Logic Jul 27, 2019

#2**+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

hectictar Jul 27, 2019