Aim: How do we solve
Final project – Jie C. Lee
The lesson is appropriate for students in 9th grade.
The resource is needed to implement my lesson is PowerPoint.
Aim: How do we solve an 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 an equation and an
inequality.
3. Solve first-degree inequalities.
4. Graph the solution on a number line.
5. Check a member of the solution.
DO NOW:
1. Insert the appropriate comparison symbol (< or >) between each pair of
numerals:
a) 6 9
b) -6 - 9
c) 6 + 3 9 + 3
d) 6 – 3 9 – 3
e) 6(3) 9(3)
f) 6(-3) 9(-3)
g) 6/-3 9/-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, the sign 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 - 2 < 10? 4x - 2 > 10? 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. 3 x - 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 an equation
and an inequality?
3. What are the differences in their solution sets?
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