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

ygeq-x+10

yleq -x+12

Step-by-step explanation:

Part 1) we have

ygeleft|x-1right|-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+1right|-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

y>5x-1 —–> first inequality

yleq-x —–> 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

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+6ygeq 60

Simplify

x+ygeq 10

ygeq-x+10 —–> inequality A

x+yleq 12

yleq -x+12 —-> inequality B

xgeq 0  —–> inequality C  

ygeq 0  —–> inequality D

The solution is the shaded area

see the attached figure