Answer:
Part 1) The points 1,2 and 4 are part of the solution
Part 2) The point 2 is not part of the solution
Part 3) Option 2. Dashed line, shade below
Part 4) The system of inequalities is
![y\geq-x+10](https://tex.z-dn.net/?f=y%5Cgeq-x%2B10)
![y\leq -x+12](https://tex.z-dn.net/?f=y%5Cleq%20-x%2B12)
Step-by-step explanation:
Part 1) we have
![y\ge\left|x-1\right|-2](https://tex.z-dn.net/?f=y%5Cge%5Cleft%7Cx-1%5Cright%7C-2)
Using a graphing tool
The graph in the attached figure
we know that
If a ordered pair is a solution of the inequality, then the ordered pair must be belong to the shaded area of the solution
Plot the points
The points , 1,2 and 4 belong to the shaded area
therefore
The points 1,2 and 4 are part of the solution
Part 2) we have
![y>\left|x+1\right|-1](https://tex.z-dn.net/?f=y%3E%5Cleft%7Cx%2B1%5Cright%7C-1)
Using a graphing tool
The graph in the attached figure
we know that
If a ordered pair is a solution of the inequality, then the ordered pair must be belong to the shaded area of the solution
Plot the points
The point 2 not belong to the shaded area
therefore
The point 2 is not part of the solution
Part 3) we have
-----> first inequality
-----> second inequality
we know that
The solution of the second inequality is the shaded area below to the dashed line
The equation of the dashed line is ![y=-x](https://tex.z-dn.net/?f=y%3D-x)
Part 4)
Let
x------> the number of hours at work as a cashier
y------> the number of hours at work as a baby sit
we know that
![6x+6y\geq 60](https://tex.z-dn.net/?f=6x%2B6y%5Cgeq%2060)
Simplify
-----> inequality A
----> inequality B
-----> inequality C
-----> inequality D
The solution is the shaded area
see the attached figure