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Warm upSolve the two-step equations.

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Homework

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Symbol Description

less than or equal to

greater than or equal to

greater than

less than

not equal to

≠

≥

>

<

≤

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You can graph a solution to an equation or an inequality on a number line.

Equation: 5=x

Inequality:X>4

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A solid circle states that the solution set will include that value.

X=-1

An open circle states that the solution set will not include that value.

X>-1

A solution for an equation requires a point (a solid dot)A solid circle states that the solution is that value.

A solution for an inequality requires a point (solid or open) and an arrow.

1 02345 1 2 3 4 5

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Pull

Pull

10 2 3 4 5 6 7 8 9 1012345678910

Graph x > 5

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Pull

Pull

10 2 3 4 5 6 7 8 9 1012345678910

Graph x > 2

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Pull

Pull

10 2 3 4 5 6 7 8 9 1012345678910

Graph x > -6

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Pull

Pull

10 2 3 4 5 6 7 8 9 1012345678910

Graph x < -1

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Pull

Pull

10 2 3 4 5 6 7 8 9 1012345678910

Graph x < -7

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Pull

Pull

10 2 3 4 5 6 7 8 9 1012345678910

Graph 4 < x(rewrite the inequality so that x is on the left)

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v is greater than 2

10 2 3 4 5 6 7 8 9 1012345678910

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homework

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Homework

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Solving Inequalities Quiz

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1 When graphing , use an open circle.

True  

False  

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2 Graph the solution set y ≥ 5/4.

A  

B  

C  

D  

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3 Which number line is the correct solution for the inequality, x  2 > 1?

A  

B  

C  

D  

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4 Solve this inequality, 3x ≤ 24

A x > 4

B x ≤ 12

C x ≤ 8

D x 

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5 Solve this inequality, x  4 ≥ 1

A x ≥ 3

B x > 2

C x ≤ 5

D x 

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6 When you multiply or divide an inequality by a negative number, you must reverse the direction of the inequality.

True  

False  

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7 Solve this inequality, 2x  2

C x ≥ 3

D x > 2

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8 Solve this inequality, x/3 

Attachments

8A014_TNG.pdf

Lesson Objectives & Teacher NotesLesson Objectives & Teacher NotesLesson Objectives & Teacher NotesLesson Objectives & Teacher NotesLesson Objectives & Teacher NotesLesson Objectives & Teacher NotesLesson Title Solving Inequalities Code 8A014 Grade 8Objective Solving inequalities and using inequalities to solve problems. Before you begin the

lesson, we recommend that you modify a Notebook line setting. This will help you to simplify the process of graphing inequalities. Click to select the Line Tool, and then click on View/Properties and select Line Style from the Properties pane. Select the dark green color in the 2nd row of the Color palette, choose the third line thickness, and from the Line Style/End drop-down menu, select the arrowhead option. Click Save Tool Properties at the bottom of the pane.

Solving inequalities and using inequalities to solve problems. Before you begin the lesson, we recommend that you modify a Notebook line setting. This will help you to simplify the process of graphing inequalities. Click to select the Line Tool, and then click on View/Properties and select Line Style from the Properties pane. Select the dark green color in the 2nd row of the Color palette, choose the third line thickness, and from the Line Style/End drop-down menu, select the arrowhead option. Click Save Tool Properties at the bottom of the pane.

Solving inequalities and using inequalities to solve problems. Before you begin the lesson, we recommend that you modify a Notebook line setting. This will help you to simplify the process of graphing inequalities. Click to select the Line Tool, and then click on View/Properties and select Line Style from the Properties pane. Select the dark green color in the 2nd row of the Color palette, choose the third line thickness, and from the Line Style/End drop-down menu, select the arrowhead option. Click Save Tool Properties at the bottom of the pane.

Solving inequalities and using inequalities to solve problems. Before you begin the lesson, we recommend that you modify a Notebook line setting. This will help you to simplify the process of graphing inequalities. Click to select the Line Tool, and then click on View/Properties and select Line Style from the Properties pane. Select the dark green color in the 2nd row of the Color palette, choose the third line thickness, and from the Line Style/End drop-down menu, select the arrowhead option. Click Save Tool Properties at the bottom of the pane.

Solving inequalities and using inequalities to solve problems. Before you begin the lesson, we recommend that you modify a Notebook line setting. This will help you to simplify the process of graphing inequalities. Click to select the Line Tool, and then click on View/Properties and select Line Style from the Properties pane. Select the dark green color in the 2nd row of the Color palette, choose the third line thickness, and from the Line Style/End drop-down menu, select the arrowhead option. Click Save Tool Properties at the bottom of the pane.

Page 1 Title page. Title page. Title page. Title page. Title page. Page 2 Ask student volunteers to graph the solutions to the inequalities on the number lines

using the cloned circles and the Line Tool. Use the Hint animation to remind students the significance of the closed circle or an open circle.

Ask student volunteers to graph the solutions to the inequalities on the number lines using the cloned circles and the Line Tool. Use the Hint animation to remind students the significance of the closed circle or an open circle.

Ask student volunteers to graph the solutions to the inequalities on the number lines using the cloned circles and the Line Tool. Use the Hint animation to remind students the significance of the closed circle or an open circle.

Ask student volunteers to graph the solutions to the inequalities on the number lines using the cloned circles and the Line Tool. Use the Hint animation to remind students the significance of the closed circle or an open circle.

Ask student volunteers to graph the solutions to the inequalities on the number lines using the cloned circles and the Line Tool. Use the Hint animation to remind students the significance of the closed circle or an open circle.

Page 3 Two worked examples which illustrate solving inequalities by addition or subtraction. Explain to students that solving inequalities is virtually the same process as solving linear equations - with the important exception that when you multiply an inequality by a negative number, (or divide by a negative), it changes the direction of the inequality.

Two worked examples which illustrate solving inequalities by addition or subtraction. Explain to students that solving inequalities is virtually the same process as solving linear equations - with the important exception that when you multiply an inequality by a negative number, (or divide by a negative), it changes the direction of the inequality.

Two worked examples which illustrate solving inequalities by addition or subtraction. Explain to students that solving inequalities is virtually the same process as solving linear equations - with the important exception that when you multiply an inequality by a negative number, (or divide by a negative), it changes the direction of the inequality.

Two worked examples which illustrate solving inequalities by addition or subtraction. Explain to students that solving inequalities is virtually the same process as solving linear equations - with the important exception that when you multiply an inequality by a negative number, (or divide by a negative), it changes the direction of the inequality.

Two worked examples which illustrate solving inequalities by addition or subtraction. Explain to students that solving inequalities is virtually the same process as solving linear equations - with the important exception that when you multiply an inequality by a negative number, (or divide by a negative), it changes the direction of the inequality.

Page 4 Solving inequalities by multiplying or dividing by a positive number. Click to animate the steps and then ask student volunteers to graph the solutions on the number line.Solving inequalities by multiplying or dividing by a positive number. Click to animate the steps and then ask student volunteers to graph the solutions on the number line.Solving inequalities by multiplying or dividing by a positive number. Click to animate the steps and then ask student volunteers to graph the solutions on the number line.Solving inequalities by multiplying or dividing by a positive number. Click to animate the steps and then ask student volunteers to graph the solutions on the number line.Solving inequalities by multiplying or dividing by a positive number. Click to animate the steps and then ask student volunteers to graph the solutions on the number line.

Page 5 Solving inequalities by multiplying or dividing by a negative number. As already noted above, when multiplying or dividing by a negative number, the inequality is reversed. Stress to students that forgetting to reverse the inequality is a very common error when solving inequalities.

Solving inequalities by multiplying or dividing by a negative number. As already noted above, when multiplying or dividing by a negative number, the inequality is reversed. Stress to students that forgetting to reverse the inequality is a very common error when solving inequalities.

Solving inequalities by multiplying or dividing by a negative number. As already noted above, when multiplying or dividing by a negative number, the inequality is reversed. Stress to students that forgetting to reverse the inequality is a very common error when solving inequalities.

Solving inequalities by multiplying or dividing by a negative number. As already noted above, when multiplying or dividing by a negative number, the inequality is reversed. Stress to students that forgetting to reverse the inequality is a very common error when solving inequalities.

Solving inequalities by multiplying or dividing by a negative number. As already noted above, when multiplying or dividing by a negative number, the inequality is reversed. Stress to students that forgetting to reverse the inequality is a very common error when solving inequalities.

Page 6 Use the Pen Tool to complete the inequality statements.Use the Pen Tool to complete the inequality statements.Use the Pen Tool to complete the inequality statements.Use the Pen Tool to complete the inequality statements.Use the Pen Tool to complete the inequality statements.Page 7 Solution to page 6.Solution to page 6.Solution to page 6.Solution to page 6.Solution to page 6.Page 8 Practice solving inequalities and graphing the solutions. You may wish to assign this

activity as a task and then ask student volunteers to share their answers at the SMART Board.

Practice solving inequalities and graphing the solutions. You may wish to assign this activity as a task and then ask student volunteers to share their answers at the SMART Board.

Practice solving inequalities and graphing the solutions. You may wish to assign this activity as a task and then ask student volunteers to share their answers at the SMART Board.

Practice solving inequalities and graphing the solutions. You may wish to assign this activity as a task and then ask student volunteers to share their answers at the SMART Board.

Practice solving inequalities and graphing the solutions. You may wish to assign this activity as a task and then ask student volunteers to share their answers at the SMART Board.

Page 9 Solution to page 8.Solution to page 8.Solution to page 8.Solution to page 8.Solution to page 8.Page 10 A contextual question that can be used for extension work. Suggest to students that

we let t represent the cost of the textbook.A contextual question that can be used for extension work. Suggest to students that we let t represent the cost of the textbook.A contextual question that can be used for extension work. Suggest to students that we let t represent the cost of the textbook.A contextual question that can be used for extension work. Suggest to students that we let t represent the cost of the textbook.A contextual question that can be used for extension work. Suggest to students that we let t represent the cost of the textbook.

Math

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