Final project – Jie C. Lee

The lesson is appropriate for students in 9thgrade.

The resource is needed to implement my lesson is PowerPoint.

Aim: How do we solvean inequality?

PERFORMANCE OBJECTIVES:

The students will be able to...

1. Recall the meaning of an inequality.

2. State the differences in the procedures for solving anequation and an

inequality.

3. Solve first-degree inequalities.

4. Graph the solution on a number line.

5. Check a member of the solution.

DONOW:

1. Insert the appropriate comparisonsymbol (< or >) between each pair of

numerals:

a) 69

b) -6- 9

c) 6 + 39 + 3

d) 6 – 39 – 3

e) 6(3)9(3)

f) 6(-3)9(-3)

g) 6/-39/-3

2. What patterns do you observe here?

PROCEDURES:

1. Students should observe that the sign of the inequality is preserved in all

cases except f and g when the numbers are multiplied or divided by the same

negative number, thesign of the inequality is reversed.

2. Two algebraic expressions joined with a sign of inequality represent an algebraic

inequality.

3. Signs of inequality include:  that means “less than”, that means “greater than”,

that means “less than or equal to”,that means “greater than or equal to and 

that means “not equal to”.

4. To solve an inequality is to find the set of numbers, called the solution set that make

the inequality true. For example, the solution set of the inequality x 1 include all

numbers greater than 1. It is represented on the number as the thick line segment

drawn to the right of number 1. Open circle above number 1 indicates that 1 is not

included in the solution set.

-1 0 1 2 3 4 5

5. Consider: 4x – 2 = 10

4x – 2 10

Find the solution set for each and graph on the number line.

4x - 2 = 10 4x - 2 10

+2 +2 +2 +2

4x = 12 4x  12

4 4 4 4

x = 3 x  3

Check: Check:

4x -2 = 10 ? 4x – 2  10

4(3) – 2 =10 ? 4(4) - 2  10 ?

12 – 2 = 10 ? 16 -2  10?

10 = 10 ☺ 1410 ☺

Graphing the Solutions:

x = 3

0 1 2 3 4 5

x  3

0 1 2 3 4 5

Question:

a. What is the similarity and the difference between solving an equation and

an inequality?

b. How would the solution set and graph change if the inequality were

changed to 4x -210? 4x -210? 4x -2  10?

c. Explain if the open or closed circle is needed to represent 3 on the number

line that shows the solution set of inequality x 3 and draw the solution set on

the number line.

6. MODEL PROBLEM: Find and graph the solution set of the inequality: 3x - 2  1

HOW TO PROCEED SOLUTION

a. Add 2 to -2 and add 2 to 1. 3x - 2  1

+ 2 + 2

b. Divide by 3 on both sides and find the solution set. 3x  3

3 3

x  1, solution set

c. Draw x  1 on the number line.

-1 0 1 2 3 4 5

7. APPLICATIONS: Solve and graph:

a) 2b – 3 > 7

b) 4d + 4  16

c) m + 2 < 0

d) 8 < d – 6

e) 5  1 – y

f) 4b -6 > 8

SUMMARY:

1. In 3 or 4 sentences, explain the meaning of the signs of inequality and why we

need to use the open or the closed circle to represent the solution set of the

inequality on the number line.

2. What are the key differences between the techniques for solving anequation

and an inequality?

3. What are the differences in their solution sets?