Answer:
[tex]b=1, \geq[/tex]
Step-by-step explanation:
we know that
The absolute value function has two solutions
Observing the graph
the solutions are
[tex]x\geq 1[/tex] and [tex]x\leq -3[/tex]
First solution (case positive)
assume the symbol of the first solution and then compare the results
[tex]\left|x+b\right|\ge2[/tex]
[tex](x+b)\ge2[/tex]
[tex]x\ge2-b[/tex]
[tex]2-b=1\\b=2-1\\ b=1[/tex]
Second solution (case negative)
[tex]-(x+b)\ge2[/tex]
Multiply by -1 both sides
[tex](x+b)\leq-2[/tex]
substitute the value of b and compare the results
[tex](x+1)\leq-2[/tex]
[tex]x\leq-2-1[/tex]
[tex]x\leq-3[/tex] -------> is correct
