Answer :
Integers 3, 4, 5 are solution to given inequality
Solution:
Given is:
[tex](x - 1) + 3\geq 5[/tex]
We have to determine whether each of the integers from -5 to 5 is a solution of the equation
Substitute x = -5
[tex]-5-1 + 3\geq 5\\\\-3\geq 5[/tex]
But the above equation is not true
Therefore, x = -5 is not a solution to given inequality
Substitute x = -4
[tex]-4-1+3\geq 5\\\\-2\geq 5[/tex]
But the above equation is not true
Therefore, x = -4 is not a solution to given inequality
Substitute x = -3
[tex]-3-1+3\geq 5\\\\-1\geq 5[/tex]
But the above equation is not true
Therefore, x = -3 is not a solution to given inequality
Substitute x = -2
[tex]-2-1+3\geq 5\\\\0\geq 5[/tex]
But the above equation is not true
Therefore, x = -2 is not a solution to given inequality
Substitute x = -1
[tex]-1-1+3\geq 5\\\\1\geq 5[/tex]
But the above equation is not true
Therefore, x = -1 is not a solution to given inequality
Substitute x = 0
[tex]0-1+3\geq 5\\\\2\geq 5[/tex]
But the above equation is not true
Therefore, x = 0 is not a solution to given inequality
Substitute x = 1
[tex]1-1+3\geq 5\\\\3\geq 5[/tex]
But the above equation is not true
Therefore, x = 1 is not a solution to given inequality
Substitute x = 2
[tex]2-1+3\geq 5\\\\1+3\geq 5\\\\4\geq 5[/tex]
But the above equation is not true
Therefore, x = 2 is not a solution to given inequality
Substitute x = 3
[tex]3-1+3\geq 5\\\\5\geq 5[/tex]
Thus the above equation is true
Therefore, x = 3 is a solution to given inequality
Substitute x = 4
[tex]4-1+3\geq 5\\\\6\geq 5[/tex]
Thus the above equation is true
Therefore, x = 4 is a solution to given inequality
Substitute x = 5
[tex]5-1+3\geq 5\\\\7\geq 5[/tex]
Thus the above equation is true
Therefore, x = 5 is a solution to given inequality