Question

1. Graph the inequality y≥2|x-1|-2. Which point is part of the solution?

Answer 1

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

$y\geq-x+10$

$y\leq -x+12$

Step-by-step explanation:

Part 1) we have

$y\ge\left|x-1\right|-2$

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

$y>\left|x+1\right|-1$

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

$y\leq-x$ -----> 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

$6x+6y\geq 60$

Simplify

$x+y\geq 10$

$y\geq-x+10$ -----> inequality A

$x+y\leq 12$

$y\leq -x+12$ ----> inequality B

$x\geq 0$  -----> inequality C  

$y\geq 0$  -----> inequality D

The solution is the shaded area

see the attached figure

Answer 2

Y > = 2 | x - 1| - 2...subbing in (1,0)
0 > = 2 | 1 - 1| - 2
0 > = 2 (0) - 2
0 > = -2...correct....so (1,0) is part of the solution
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y > | x + 1| - 1...subbing in (1,1)
1 > | 1 + 1| - 1
1 > 2 - 1
1 > 1....incorrect....so (1,1) is not part of the solution
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less then or equal....dashed line, shaded below
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x = cashier job hrs, y = babysitting hrs
y > = 0
x > = 0
6x + 6y = 60
x < = 12
y < = 12