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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
A - A = Area of shaded region
12(10) – 12(10) = Area of green region
2
Solution
Find the area of the green shaded region.Problem 2
10
12
A - A = Area of shaded region
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
Solution
To get the top number
Multiply 1/3 and 3/5 together.
Solve the diamond problem.Problem 3
1 3
3 5
Solution
1*5
3*5 +
=
3
5
Multiply top and bottom by 5.
1
5
Solve the diamond problem.Problem 3
1 3
3 5
Solution
1*5 5
3*5 15+
=
3
5
1
5
Multiply top and bottom by 5.
Solve the diamond problem.Problem 3
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
Solve the diamond problem.Problem 3
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
Use the graph to answer each of the questions.
Name the y-coordinate of the point whose x-coordinate is -1.
Problem 5
Use the graph to answer each of the questions.
Name the y-coordinate of the point whose x-coordinate is -1.
The y-coordinate = + 2
Problem 5
-1
2
Solution
Use the graph to answer each of the questions.
Name the x-coordinate of the point whose y-coordinate is -4.
Problem 6
Use the graph to answer each of the questions.
Name the x-coordinate of the point whose y-coordinate is -4.
Problem 6
The x-coordinate = + 1
Solution
Use the graph to answer each of the questions.
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
4 laps 1 lap
6 min. x min=
If George runs 4 laps in 6 minutes. At that pace how long did it take him to run 1 lap?
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
4 laps .5 lap
6 min. x min=
If George runs 4 laps in 6 minutes. At that pace how long did it take him to run 1/2 lap?
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
4 laps x lap
6 min. 30 min=
If George runs 4 laps in 6 minutes. How many laps would George run if he ran 30 minutes?
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
+8 - 12 - 5
-4 - 5
- 9
Solution
Calculate the using the order of operations.Problem 12
30 – (17 – 5 • 2)²
30 – (17 – 10) ²
1st Multiply negative 5 and positive
Solution
Calculate the using the order of operations.Problem 12
30 – (17 – 5 • 2)²
30 – (17 – 10) ²
30 – (7) ²
1st Multiply negative 5 and positive
2nd Subtract 17 and 10
Solution
Calculate the using the order of operations.Problem 12
30 – (17 – 5 • 2)²
30 – (17 – 10) ²
30 – (7) ²
30 – 49
1st Multiply negative 5 and positive
2nd Subtract 17 and 10
3rd Square 7
Solution
Calculate the using the order of operations.Problem 12
30 – (17 – 5 • 2)²
30 – (17 – 10) ²
30 – (7) ²
30 – 49
- 19
1st Multiply negative 5 and positive
2nd Subtract 17 and 10
3rd Square 7
4th Subtract
Solution
Calculate the using the order of operations.Problem 13
4(2 + 5 – 3 • 2) ÷ (3² – 2² )
4(2 + 5 – 6) ÷ ( 9 – 4 )
Solution
Do the operations in blue 1st
Calculate the using the order of operations.Problem 13
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.
Calculate the using the order of operations.Problem 13
4(2 + 5 – 3 • 2) ÷ (3² – 2² )
4(2 + 5 – 6) ÷ ( 9 – 4 )
4(7 – 6 ) ÷ (5)
4(1) ÷ 5
Solution
Follow each step by doing the operations in blue.
Calculate the using the order of operations.Problem 13
4(2 + 5 – 3 • 2) ÷ (3² – 2² )
4(2 + 5 – 6) ÷ ( 9 – 4 )
4(7 – 6 ) ÷ (5)
4(1) ÷ 5
Solution
Follow each step by doing the operations in blue.
Calculate the using the order of operations.Problem 13
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
Follow each step by doing the operations in blue.
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.
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
Solve for x.Problem 15
17 + 2 – 3x = -19
19 - 3x = - 19
Solution
Combine 17 and 2 on the left side of the equal sign.
Solve for x.Problem 15
17 + 2 – 3x = -19
19 - 3x = - 19
- 19 = -19
Solution
Subtract 19 from both sides.
Solve for x.Problem 15
17 + 2 – 3x = -19
19 - 3x = - 19
- 19 = - 19
- 3x = - 38
Solution
Remember -19 -19 = - 38!
Solve for x.Problem 15
17 + 2 – 3x = -19
19 - 3x = - 19
- 19 = - 19
- 3x = - 38
Solution
Divide both sides by -3.
-3 - 3
Solve for x.Problem 15
17 + 2 – 3x = -19
19 - 3x = - 19
- 19 = - 19
- 3x = - 38
Solution
Divide both sides by -3.
-3 - 3
x = + 12.67
Solve for x.Problem 16
5x – 7 = - 1(6x – 15) Write the negative 1 before the parenthesis!!!!
Solution
Solve for x.Problem 16
5x – 7 = - 1(6x – 15)
5x – 7 = - 6x + 15
Multiply 6x and negative 15 by negative 1. That changes the signs.
Solution
Solve for x.Problem 16
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
Solve for x.Problem 16
5x – 7 = - (6x – 15)
5x – 7 = - 6x + 15
+6x + 7 = +6x + 7
Lastly divide both sides by 11.
11x = 22
Solution
Solve for x.Problem 16
5x – 7 = - (6x – 15)
5x – 7 = - 6x + 15
+6x + 7 = +6x + 7
Lastly divide both sides by 11.
11x = 22
11 11
x = 2Solution
Solve for x.Problem 17
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
Solve for x.Problem 17
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
Solve for x.Problem 17
12 – 4x + 2 = 10 – 5x + 6
14 – 4x = 16 – 5x
-14 + 5x = -14 + 5x
Solution
x = 2
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.
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
Evaluate the expression when x = - 4.Problem 23
Multiply 4 and negative 4
Multiply Positive 2 and negative 4
4x – 8 + 2x + 10
4(-4) – 8 + 2(-4) + 10
Solution
Evaluate the expression when x = - 4.Problem 23
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
Evaluate the expression when x = - 4.Problem 23
Combine left to right
4x – 8 + 2x + 10
4(-4) – 8 + 2(-4) + 10
-16 – 8 – 8 + 10
- 24 - 8 + 10
Solution
Evaluate the expression when x = - 4.Problem 23
Combine left to right
4x – 8 + 2x + 10
4(-4) – 8 + 2(-4) + 10
-16 – 8 – 8 + 10
- 24 - 8 + 10
- 32 + 10
Solution
Evaluate the expression when x = - 4.Problem 23
Combine left to right
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 4
Solution
y = -2(-2)
y = + 4
Fill the table for the rule y = -2x.
Then graph the line.
Problem 24
x -2 -1 0 1 2
y 4 2
Solution
y = -2(-1)
y = + 2
Fill the table for the rule y = -2x.
Then graph the line.
Problem 24
x -2 -1 0 1 2
y 4 2 0
Solution
y = -2(0)
y = 0
Fill the table for the rule y = -2x.
Then graph the line.
Problem 24
x -2 -1 0 1 2
y 4 2 0 -2
Solution
y = -2(1)
y = -2
Fill the table for the rule y = -2x.
Then graph the line.
Problem 24
x -2 -1 0 1 2
y 4 2 0 -2 -4
Solution
y = -2(2)
y = -4
Fill the table for the rule y = -2x.
Then graph the line.
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. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5
Solution
Problem 25
Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5
Solution
Complete the table.
x 0 1 2 3 4 5
y 2 3 4 5 6
Problem 25
Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5
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
Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5
Solution
x 0 1 2 3 4 5
y 2 3 4 5 6
How many tiles will the 50th figure have?