Label the points where the graph crosses the x-axis. x y Problem 1

Label the points where the graph crosses the x-axis. x-2012 y3210 Problem 1 Solution

Find the area of the green shaded region. Problem

Find the area of the green shaded region. Problem A - A = Area of shaded region Solution

Find the area of the green shaded region. Problem 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 A - A = Area of shaded region 12(10) – 12(10) = Area of green region – 60 = Area of green region 60 = Area of green region Solution

Solve the diamond problem. Problem

Solve the diamond problem. Problem Solution To get the top number Multiply 1/3 and 3/5 together.

Solve the diamond problem. Problem Solution = 3 15 or 1515

Solve the diamond problem. Problem Solution 1*5 3*5 + = 3535 Multiply top and bottom by

Solve the diamond problem. Problem Solution 1*5 5 3* = Multiply top and bottom by 5.

Solve the diamond problem. Problem Solution 1*5 5 3* = 3*3 5*3 Multiply top and bottom by 3. =

Solve the diamond problem. Problem Solution 1*5 5 3* = 3*3 5*3 Lastly add the two fractions. =

Solve the diamond problem. Problem Solution

Solve the diamond problem. Problem

Solve the diamond problem. Problem Think, -2 * what number = 20

Solve the diamond problem. Problem * -10 = + 20

Solve the diamond problem. Problem * -10 = + 20

Solve the diamond problem. Problem (-10) = - 12

Solve the diamond problem. Problem Solution

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 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

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

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

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

Calculate the using the order of operations. Problem 11 (-4)(-2) – 6(2)

Calculate the using the order of operations. Problem 11 (-4)(-2) – 6(2) Solution

Calculate the using the order of operations. Problem – (17 – 5 2)²

Calculate the using the order of operations. Problem – (17 – 5 2)² 30 – (17 – 10) ² 1 st Multiply negative 5 and positive Solution

Calculate the using the order of operations. Problem – (17 – 5 2)² 30 – (17 – 10) ² 30 – (7) ² 1 st Multiply negative 5 and positive 2 nd Subtract 17 and 10 Solution

Calculate the using the order of operations. Problem – (17 – 5 2)² 30 – (17 – 10) ² 30 – (7) ² 30 – 49 1 st Multiply negative 5 and positive 2 nd Subtract 17 and 10 3 rd Square 7 Solution

Calculate the using the order of operations. Problem – (17 – 5 2)² 30 – (17 – 10) ² 30 – (7) ² 30 – st Multiply negative 5 and positive 2 nd Subtract 17 and 10 3 rd Square 7 4 th Subtract Solution

Calculate the using the order of operations. Problem 13 4(2 + 5 – 3 2) ÷ (3² – 2² )

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 ÷ 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 x = x – 9

Solve for x. Combine the same color terms on each side of the equal sign Problem 14 3x x = x – 9 4x + 5 = 2x + 6 Solution

Solve for x. Subtract the 2x from each side and subtract 5 from each side. Problem 14 3x x = x – 9 4x + 5 = 2x x – 5 = -2x - 5 Solution

Solve for x. Problem 14 3x x = x – 9 4x + 5 = 2x x – 5 = -2x – 5 2x = 1 Solution

Solve for x. Divide remaining terms by 2. And the answer is.... One Half!! Problem 14 3x x = x – 9 4x + 5 = 2x x – 5 = -2x – 5 2x = 1 2 x = 1/2 Solution

Solve for x. Problem – 3x = -19

Solve for x. Problem – 3x = x = - 19 Solution Combine 17 and 2 on the left side of the equal sign.

Solve for x. Problem – 3x = x = = -19 Solution Subtract 19 from both sides.

Solve for x. Problem – 3x = x = = x = - 38 Solution Remember = - 38!

Solve for x. Problem – 3x = x = = x = - 38 Solution Divide both sides by

Solve for x. Problem – 3x = x = = x = - 38 Solution Divide both sides by x =

Solve for x. Problem 16 5x – 7 = - (6x – 15)

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 x + 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 x + 7 = +6x + 7 Lastly divide both sides by x = 22 Solution

Solve for x. Problem 16 5x – 7 = - (6x – 15) 5x – 7 = - 6x x + 7 = +6x + 7 Lastly divide both sides by x = x = 2 Solution

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

Solve for x. Problem – 4x + 2 = 10 – 5x – 4x = 16 – 5x Now get all teal colored x terms on the left and black numbers on the right. Solution

Solve for x. Problem – 4x + 2 = 10 – 5x – 4x = 16 – 5x x = x Add 5x to both sides and Subtract 14 from both sides. Solution

Solve for x. Problem – 4x + 2 = 10 – 5x – 4x = 16 – 5x x = x 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

Solve for x. Problem 20 3/2 x + 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 = = - 7 Solution 3 2 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 = = - 7 Solution 3 2 x =

Solve for x. Remember that 2/3 * 3/2 = 1. Problem 20 3/2 x + 7 = = - 7 Solution 3 2 x = x = 40/3

Complete the table. Then find the rule. Problem 21 x y-5315

Evaluate the expression when x = - 4. Problem 23 4x – 8 + 2x + 10 Replace x with -4

Evaluate the expression when x = - 4. Problem 23 Multiply 4 and negative 4 Multiply Positive 2 and negative 4 4x – 8 + 2x (-4) – 8 + 2(-4) + 10 Solution

Evaluate the expression when x = - 4. Problem 23 4x – 8 + 2x (-4) – 8 + 2(-4) – 8 – 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 (-4) – 8 + 2(-4) – 8 – Solution

Evaluate the expression when x = - 4. Problem 23 Combine left to right 4x – 8 + 2x (-4) – 8 + 2(-4) – 8 – Solution

Evaluate the expression when x = - 4. Problem 23 Combine left to right 4x – 8 + 2x (-4) – 8 + 2(-4) – 8 – Solution

Fill the table for the rule y = -2x. Then graph the line. Problem 24 x-2012 y

Fill the table for the rule y = -2x. Then graph the line. Problem 24 x-2012 y4 Solution y = -2(-2) y = + 4

Fill the table for the rule y = -2x. Then graph the line. Problem 24 x-2012 y42 Solution y = -2(-1) y = + 2

Fill the table for the rule y = -2x. Then graph the line. Problem 24 x-2012 y420 Solution y = -2(0) y = 0

Fill the table for the rule y = -2x. Then graph the line. Problem 24 x-2012 y420-2 Solution y = -2(1) y = -2

Fill the table for the rule y = -2x. Then graph the line. Problem 24 x-2012 y Solution y = -2(2) y = -4

Fill the table for the rule y = -2x. Then graph the line. Problem 24 x-2012 y Solution Now, plot the points and graph the line.

Study the tiles. Draw the 1 st, and 5 th figures. Problem 25 Fig. 2 Fig. 3 Fig. 4

Study the tiles. Draw the 1 st, and 5 th 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 y

Problem 25 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Solution Complete the table. x y23456

Problem 25 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Solution x y23456 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 y23456 How many tiles will the 50 th figure have?

Problem 25 Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Solution x y23456 How many tiles will the 50 th figure have? y = The 50 th figure will have 51 tiles.