Answer:
[tex]\mid x+3\mid\ge 2[/tex]
Step-by-step explanation:
Inequalities
The solution for the inequality:
[tex]\mid x+a\mid\ge b[/tex]
Can be expressed as:
[tex]x+a\ge b[/tex]
OR:
[tex]x+a\le -b[/tex]
Subtracting a to both inequalities:
[tex]x\ge b-a[/tex]
[tex]x\le -b-a[/tex]
Comparing to the given solutions, we have:
[tex]b-a=-1[/tex]
[tex]-b-a=-5[/tex]
Adding both equations:
[tex]-2a=-6[/tex]
Solving:
a=3
b=2
Thus, the required inequality form is:
[tex]\mathbf{\mid x+3\mid\ge 2}[/tex]
