label the points where the graph crosses the x-axis. x y problem 1

Label the points where the graph crosses the x-axis.

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x

y

Problem 1

Label the points where the graph crosses the x-axis.

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x -2 -1 0 1 2

y 3 2 1 0 -1

Problem 1

Solution

Find the area of the green shaded region.Problem 2

10

12


10

12

A - A = Area of shaded region

Solution


10

12


12(10) – 12(10) = Area of green region

2

Solution


10

12


12(10) – 12(10) = Area of green region

2

120 – 60 = Area of green region

60 = Area of green region

Solution

Solve the diamond problem.Problem 3

1 3

3 5


1 3

3 5

Solution

To get the top number

Multiply 1/3 and 3/5 together.


1 3

3 5

Solution

1 3

3 5• =

3

15or

1

5


1 3

3 5

Solution

1*5

3*5 +

=

3

5

Multiply top and bottom by 5.

1

5


1 3

3 5

Solution

1*5 5

3*5 15+

=

3

5

1

5

Multiply top and bottom by 5.


1 3

3 5

Solution

1*5 5

3*5 15+

=

3*3

5*3

Multiply top and bottom by 3.= 9

15

1

5


1 3

3 5

Solution

1*5 5

3*5 15+

=

3*3

5*3

Lastly add the two fractions.

= 9

15

14

15

1

5


1 3

3 5

Solution

14

15

1

5


20

-2


20

-2

Think, -2 * what number = 20


20

-2

-2 * -10 = + 20


20

-2 - 10

-2 * -10 = + 20


20

-2 - 10

-2 + (-10) = - 12


20

-2 - 10

-12

Solution

Use the graph to answer each of the questions.

Name the y-coordinate of the point whose x-coordinate is -1.

Problem 5


Name the y-coordinate of the point whose x-coordinate is -1.

The y-coordinate = + 2

Problem 5

-1

2

Solution


Name the x-coordinate of the point whose y-coordinate is -4.

Problem 6


Name the x-coordinate of the point whose y-coordinate is -4.

Problem 6

The x-coordinate = + 1

Solution


Label the point where the graph crosses the x-axis.

Problem 7

The graph crosses at - .4

Solution

If George runs 4 laps in 6 minutes. At that pace how long did it take him to run 1 lap?

Problem 8


Problem 8

4 laps 1 lap

6 min. x min=


Problem 8

4 laps 1 lap

6 min. x min=

One lap takes George 6/4 or 3/2 minutes.

Solution

If George runs 4 laps in 6 minutes. At that pace how long did it take him to run 1/2 lap?

Problem 9


Problem 9

4 laps .5 lap

6 min. x min=


Problem 9

4 laps .5 lap

6 min. x min=

It will take ¾ min to run a ½ lap.

Solution

If George runs 4 laps in 6 minutes. How many laps would George run if he ran 30 minutes?

Problem 10


Problem 10

4 laps x lap

6 min. 30 min=


Problem 10

4 laps x lap

6 min. 30 min=

After 30 minutes of running, George will have run 20 laps!

Solution

Calculate the using the order of operations.Problem 11

(-4)(-2) – 6(2) - 5


(-4)(-2) – 6(2) - 5

+8 - 12 - 5


(-4)(-2) – 6(2) - 5

+8 - 12 - 5

-4 - 5

- 9

Solution


30 – (17 – 5 • 2)²


30 – (17 – 5 • 2)²

30 – (17 – 10) ²

1st Multiply negative 5 and positive

Solution


30 – (17 – 5 • 2)²

30 – (17 – 10) ²

30 – (7) ²


2nd Subtract 17 and 10

Solution


30 – (17 – 5 • 2)²

30 – (17 – 10) ²

30 – (7) ²

30 – 49



3rd Square 7

Solution


30 – (17 – 5 • 2)²

30 – (17 – 10) ²

30 – (7) ²

30 – 49

- 19



3rd Square 7

4th Subtract

Solution


4(2 + 5 – 3 • 2) ÷ (3² – 2² )


4(2 + 5 – 3 • 2) ÷ (3² – 2² )

4(2 + 5 – 6) ÷ ( 9 – 4 )

Solution

Do the operations in blue 1st


4(2 + 5 – 3 • 2) ÷ (3² – 2² )

4(2 + 5 – 6) ÷ ( 9 – 4 )

4(7 – 6 ) ÷ (5)

Solution

Follow each step by doing the operations in blue.


4(2 + 5 – 3 • 2) ÷ (3² – 2² )

4(2 + 5 – 6) ÷ ( 9 – 4 )

4(7 – 6 ) ÷ (5)

4(1) ÷ 5

Solution



4(2 + 5 – 3 • 2) ÷ (3² – 2² )

4(2 + 5 – 6) ÷ ( 9 – 4 )

4(7 – 6 ) ÷ (5)

4(1) ÷ 5

4 ÷ 5

0.80 Solution


Solve for x.

Combine the same color terms

on each side of the equal sign

Problem 14

3x + 5 + x = 15 + 2x – 9

Solve for x.

Combine the same color terms

on each side of the equal sign

Problem 14

3x + 5 + x = 15 + 2x – 9

4x + 5 = 2x + 6

Solution

Solve for x.

Subtract the 2x from each side

and subtract 5 from each side.

Problem 14

3x + 5 + x = 15 + 2x – 9

4x + 5 = 2x + 6

-2x – 5 = -2x - 5

Solution

Solve for x.Problem 14

3x + 5 + x = 15 + 2x – 9

4x + 5 = 2x + 6

-2x – 5 = -2x – 5

2x = 1

Solution

Solve for x.

Divide remaining terms by 2.

And the answer is . . . .

One Half!!

Problem 14

3x + 5 + x = 15 + 2x – 9

4x + 5 = 2x + 6

-2x – 5 = -2x – 5

2x = 1

2 2

x = 1/2Solution


17 + 2 – 3x = -19


17 + 2 – 3x = -19

19 - 3x = - 19

Solution

Combine 17 and 2 on the left side of the equal sign.


17 + 2 – 3x = -19

19 - 3x = - 19

- 19 = -19

Solution

Subtract 19 from both sides.


17 + 2 – 3x = -19

19 - 3x = - 19

- 19 = - 19

- 3x = - 38

Solution

Remember -19 -19 = - 38!


17 + 2 – 3x = -19

19 - 3x = - 19

- 19 = - 19

- 3x = - 38

Solution

Divide both sides by -3.

-3 - 3


17 + 2 – 3x = -19

19 - 3x = - 19

- 19 = - 19

- 3x = - 38

Solution

Divide both sides by -3.

-3 - 3

x = + 12.67


5x – 7 = - (6x – 15)


5x – 7 = - 1(6x – 15) Write the negative 1 before the parenthesis!!!!

Solution


5x – 7 = - 1(6x – 15)

5x – 7 = - 6x + 15

Multiply 6x and negative 15 by negative 1. That changes the signs.

Solution


5x – 7 = - (6x – 15)

5x – 7 = - 6x + 15

+6x + 7 = +6x + 7

Add 6x to both sides and add 7 to both sides of the equal sign.

Solution


5x – 7 = - (6x – 15)

5x – 7 = - 6x + 15

+6x + 7 = +6x + 7

Lastly divide both sides by 11.

11x = 22

Solution


5x – 7 = - (6x – 15)

5x – 7 = - 6x + 15

+6x + 7 = +6x + 7

Lastly divide both sides by 11.

11x = 22

11 11

x = 2Solution


12 – 4x + 2 = 10 – 5x + 6Combine the black non-x terms.


12 – 4x + 2 = 10 – 5x + 6

14 – 4x = 16 – 5x

Now get all teal colored x terms on the left and black numbers on the right.

Solution


12 – 4x + 2 = 10 – 5x + 6

14 – 4x = 16 – 5x

-14 + 5x = -14 + 5x

Add 5x to both sides and

Subtract 14 from both sides.

Solution


12 – 4x + 2 = 10 – 5x + 6

14 – 4x = 16 – 5x

-14 + 5x = -14 + 5x

Solution

x = 2

Simplify.Problem 19

5x + 7 – (2x + 2)

Simplify.Problem 18

5x + 7 –1(2x + 2) Write the negative 1 before the parenthesis!!!!

Solution

Simplify.Problem 18

5x + 7 –1(2x + 2)

5x + 7 – 2x – 2

Change the signs in front of the 2x and 2!!

Solution

Simplify.Problem 18

5x + 7 –1(2x + 2)

5x + 7 – 2x – 2

3x + 5

Since there is NO equal sign, simply combine like terms.

Solution

Solve for x.

Subtract 7 from sides

Problem 20

3/2 x + 7 = 27


3/2 x + 7 = 27

- 7 = - 7

Solution

Subtract 7 from sides

Solve for x.

Stop! There is a fraction in front of the x.

We solve it by multiplying both sides by 2/3.

Problem 20

3/2 x + 7 = 27

- 7 = - 7

Solution

32

x = 20

Solve for x.

Stop! There is a fraction in front of the x.

We solve it by multiplying both sides by 2/3.

Problem 20

3/2 x + 7 = 27

- 7 = - 7

Solution

32

x = 20 2 23 3

Solve for x.

Remember that

2/3 * 3/2 = 1.

Problem 20

3/2 x + 7 = 27

- 7 = - 7

Solution

32

x = 20 2 23 3

1x = 40/3

Complete the table.

Then find the rule.

Problem 21

x -2 -1 0 1 2 3

y -5 3 15

Evaluate the expression when x = - 4.Problem 23

4x – 8 + 2x + 10 Replace x with -4


Multiply 4 and negative 4

Multiply Positive 2 and negative 4

4x – 8 + 2x + 10

4(-4) – 8 + 2(-4) + 10

Solution


4x – 8 + 2x + 10

4(-4) – 8 + 2(-4) + 10

- 16 – 8 – 8 + 10

Solution

Multiply 4 and negative 4

Multiply Positive 2 and negative 4


Combine left to right

4x – 8 + 2x + 10

4(-4) – 8 + 2(-4) + 10

-16 – 8 – 8 + 10

- 24 - 8 + 10

Solution



4x – 8 + 2x + 10

4(-4) – 8 + 2(-4) + 10

-16 – 8 – 8 + 10

- 24 - 8 + 10

- 32 + 10

Solution



4x – 8 + 2x + 10

4(-4) – 8 + 2(-4) + 10

-16 – 8 – 8 + 10

- 24 - 8 + 10

- 32 + 10

- 22Solution

Fill the table for the rule y = -2x.

Then graph the line.

Problem 24

x -2 -1 0 1 2

y



Problem 24

x -2 -1 0 1 2

y 4

Solution

y = -2(-2)

y = + 4



Problem 24

x -2 -1 0 1 2

y 4 2

Solution

y = -2(-1)

y = + 2



Problem 24

x -2 -1 0 1 2

y 4 2 0

Solution

y = -2(0)

y = 0



Problem 24

x -2 -1 0 1 2

y 4 2 0 -2

Solution

y = -2(1)

y = -2



Problem 24

x -2 -1 0 1 2

y 4 2 0 -2 -4

Solution

y = -2(2)

y = -4



Problem 24

x -2 -1 0 1 2

y 4 2 0 -2 -4

Solution

Now, plot the points and graph the line.

Study the tiles. Draw the 1st, and 5th figures.Problem 25

Fig. 2 Fig. 3 Fig. 4

Study the tiles. Draw the 1st, and 5th figures.Problem 25

Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5

Solution

Problem 25


Solution

Complete the table.

x 0 1 2 3 4 5

y

Problem 25


Solution

Complete the table.

x 0 1 2 3 4 5

y 2 3 4 5 6

Problem 25


Solution

x 0 1 2 3 4 5

y 2 3 4 5 6

Write the rule for the table.

Rule: y = x + 1 or in words

Add 1 to x to get y.

Problem 25


Solution

x 0 1 2 3 4 5

y 2 3 4 5 6

How many tiles will the 50th figure have?

Problem 25


Solution

x 0 1 2 3 4 5

y 2 3 4 5 6

How many tiles will the 50th figure have?

y = 50 + 1

The 50th figure will have 51 tiles.

label the points where the graph crosses the x-axis. x y problem 1

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