Lesson Plan-solvingLesson Plan-solving an inequalityan inequality

By Jie C. LeeBy Jie C. Lee

Aim: How do we solve an inequality? 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?

Let’s review of inequality signs

• Less Than

• Greater Than

• Less than or Equal to

• Greater than or Equal to

<>

How do we use the Number Line?

• Where do we locate the positive/larger numbers?

• Where do we locate the negative/smaller numbers?

-4 -3 -2 -1 0 1 2 3 4

Graphing on the Number Line

• When do you use the open circle? • Greater than or Less than

• Example: x > 1

-4 -3 -2 -1 0 1 2 3 4

When do you use the closed circle?Greater than or equal to or Less than or equal toExample: x -1

-3 -2 -1 0 1 2 3 4

Solving Inequalities Is Like

Solving Equations4x - 2 = 10

+2 +2

4x = 12 4 4

x = 3

4x - 2 10 +2 +2

4x 12

4 4 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 = 3x = 3

x x 3 3• What is the similarity and the difference between

solving an equation and an inequality?• How would the solution set and graph change if

the inequality were changed to 4x - 2 < 10? 4x - 2 > 10? 4x - 2 10?

• 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.

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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 3x 3 find the solution set. 3 3 x 1 c. Draw x 1 on the number line

-1 0 1 2 3 4 5

APPLICATIONS

Solve and graph: a) 2b – 3 > 7 b) 4d + 4 16c) m + 2 < 0d) 8 < d – 6 e) 5 1 – yf) 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?