Question

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

1. (3,0)
2. (1,0)
3. (0,-3)
4. (-1,0)

2. Graph the inequality y>|x+1|-1. Which point is NOT part of the solution?

1. (-1,0)
2. (1,1)
3. (-1,2)
4. (1,3)

3. Given {y>5x-1
y≤-x Which of the following describes the boundary line and shading for the second inequality in the system?

4. Dashed line, shade above
2. Dashed line, shade below
3. Solid line, shade above
4. solid line, shade below

5. You work as a cashier for a bookstore and earn $6 per hour. You also baby sit and earn $6 per hour. You want to earn $60 per week, but would like to work no more than 12 hours per week.

Which system of inequalities, along with y≥0 and x≥0, would you use to solve the real-world problem?

Answer 1

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
=====================
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
=====================
less then or equal....dashed line, shaded below
=====================
x = cashier job hrs, y = babysitting hrs
y > = 0
x > = 0
6x + 6y = 60
x < = 12
y < = 12

Answer 2

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`

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