The lesson plan summarizes teaching students how to solve linear equations and inequalities involving absolute value. It includes learning objectives, concepts, materials, strategies, and sample problems. The lesson will begin with a review of absolute value concepts and properties. Students will then work through examples of solving absolute value equations and inequalities as a class and independently. Formative assessment includes students presenting solutions on the board and a quiz to evaluate understanding. The homework assignment is to study word problems involving numbers, integers, ages, and distances.

1. 1 | 4
Lesson Plan for Grade 7 Mathematics
I. TOPIC: Solving Linear Equations and Inequalities in One Variable Involving Absolute Value
II. Learning Objectives
At the end of the lesson, the students must have:
a. solved linear equations and inequalities in one variable involving absolute value
III. Learning Contents
A. Mathematical Concepts
 First degree equations and inequalities, absolute value
B. References
Alferez M. & Duro, M.C. (2007). MSA intermediate algebra. Quezon City: MSA Publishing House
C. Instructional Materials
Chalk, Blackboard, Manila Paper, Cartolina, Marker, Visual Aids
D. Value Foci
Accuracy, Cooperation, Objectivity, Perseverance
E. Strategies/Techniques
Discussion Method, Oral Questioning, Constructivism, Cooperative Learning, Deductive Method
IV. Learning Activities
A. Preliminaries
Teacher’s Activity Students’ Activity
a. Prayer
May I request everyone to stand for a prayer?
Good morning class!
Please take your seat.
b. Checking of Attendance
(Stands up and pray)
Good morning Maám!
Thank you, Maám.
B. Developmental Activities
Teacher’s Activity Students’ Activity
a. Activity
Today, we will now involve absolute value in
solving equations and inequalities. Let us first
review absolute value. Please answer the following.
I will give you 5 minutes for this. Is my instruction
clear?
1. What is an absolute value?
2. What is the absolute value of -8?
3. What is the absolute value of 8?
4. What can you conclude in items 2 and 3?
5. What is the absolute value of 0?
6. In getting the absolute value of a number,
what is the resulting sign? Is it positive or
negative?
b. Analysis
Are you all done?
Now, what is an absolute value?
Yes, Maám.
Yes, Maám.

2. 2 | 4
Very good. What is your answer in number 2 and
3?
Very good. Now, what can you conclude?
Very good. What about in number 5?
Very good. What about in number 6?
Very good, now let’s start the discussion on
solving.
I have examples of equations and inequalities
involving absolute value.
1. | 𝑥| = 9
2. |2𝑥 − 4| = 6
3. |3𝑥 + 5| = −6
4. 2|4𝑥 − 10| + 14 = 2
5. |3𝑥 + 1| = |2𝑥 − 7|
6. | 𝑥 + 5| − 6 ≤ −2
7. |2𝑥 − 7| ≥ 19
Class, let’s start with number 1. Now, what number
in the number line that is 9 units far from 0?
Very good. That means 𝑥 = −9 or 𝑥 = 9.
What about in number 2?
Before we solve this, remember this property.
Please let us read.
Is 6 a positive number?
Now, what is the equivalent of this equation?
Very good. Now, who wants to solve these?
Yes, ___ and ___.
Very good. Do you know what happens if 𝑘 is a
negative number? Is it possible to have a negative
distance?
Very good. That means there is no solution to
equations with negative 𝑘. Now, what is the
solution for number 3?
Very good. Now who wants to try number 4?
Yes, ___.
Very good. Now, let’s have number 5. To solve this
equation, let’s read the rule first.
The distance of each point from 0 is defined as
the absolute value of the number and denoted by
| 𝑥|.
Both 8, Maám.
They’re the same.
0, Maám.
Positive, Maám.
9 and -9, Maám.
| 𝑎𝑥 + 𝑏| = 𝑘 is equivalent to 𝑎𝑥 + 𝑏 = 𝑘 or 𝑎𝑥 +
𝑏 = −𝑘, where 𝑘 is a positive number.
Yes, Maám.
2𝑥 − 4 = 6 or 2𝑥 − 4 = −6, Maám.
(Raising hands)
𝑥 = 5 or 𝑥 = −1
No, Maám.
No solution/Empty set.
(Raising hands)
2|4𝑥 − 10| + 14 = 2
2|4𝑥 − 10| = 2 − 14
2|4𝑥 − 10| = −12
|4𝑥 − 10| = −6
Since 𝑘 = −6, the equation has no solution.
To solve an absolute value equation of the form
| 𝑎𝑥 + 𝑏| = | 𝑐𝑥 + 𝑑|, solve for the equations 𝑎𝑥 +
𝑏 = 𝑐𝑥 + 𝑑 and 𝑎𝑥 + 𝑏 = −(𝑐𝑥 + 𝑑). The solution
set is the union of the solution sets of these
equations.

3. 3 | 4
Following what you read, who wants to solve
number 5?
Yes, ___.
Very good ___. Now, let’s try inequalities. Please
read the following rules on the board.
Following what you read and what you’ve learned.
Let us solve number 6.
Class, can you follow?
In number 7, what rule should we use to solve this
inequality? Is it rule number 1 or 2?
Very good, who wants to solve this?
Yes, ___.
Class, do you have questions?
(Raising hands)
|3𝑥 + 1| = |2𝑥 − 7|
3𝑥 + 1 = 2𝑥 − 7 or 3𝑥 + 1 = −(2𝑥 − 7)
𝑥 = −8 or 𝑥 = 6/5
Let 𝑘 be a positive number, and 𝑝 and 𝑞 be two
numbers.
1. To solve | 𝑎𝑥 + 𝑏| > 𝑘, solve the compound
inequality for 𝑥
𝑎𝑥 + 𝑏 > 𝑘 or 𝑎𝑥 + 𝑏 < −𝑘.
2. To solve | 𝑎𝑥 + 𝑏| < 𝑘, solve the compound
inequality for 𝑥
−𝑘 < 𝑎𝑥 + 𝑏 < 𝑘.
| 𝑥 + 5| − 6 ≤ −2
| 𝑥 + 5| ≤ −2 + 6
| 𝑥 + 5| ≤ 4
−4 ≤ 𝑥 + 5 ≤ 4
−4 − 5 ≤ 𝑥 ≤ 4 − 5
−9 ≤ 𝑥 ≤ −1
Yes, Maám.
Number 1, Maám.
(Raising hands)
|2𝑥 − 7| ≥ 19
2𝑥 − 7 ≥ 19 or 2𝑥 − 7 ≤ −19
𝑥 ≥ 13 or 𝑥 ≤ −6
None, Maám.
C. Abstraction
Teacher’s Activity Students’ Activity
If none, let us again review the rules on solving
inequalities involving absolute values.
In solving | 𝑎𝑥 + 𝑏| = 𝑘, where 𝑘 is a positive
number, what is this equation equivalent to?
Very good. What about | 𝑎𝑥 + 𝑏| = | 𝑐𝑥 + 𝑑|?
Very good again. What about | 𝑎𝑥 + 𝑏| > 𝑘?
Very good. Lastly, what about | 𝑎𝑥 + 𝑏| < 𝑘?
Very good. Do you have any questions?
𝑎𝑥 + 𝑏 = 𝑘 or 𝑎𝑥 + 𝑏 = −𝑘, Maám.
𝑎𝑥 + 𝑏 = 𝑐𝑥 + 𝑑 and 𝑎𝑥 + 𝑏 = −(𝑐𝑥 + 𝑑), Maám.
𝑎𝑥 + 𝑏 > 𝑘 or 𝑎𝑥 + 𝑏 < −𝑘, Maám.
−𝑘 < 𝑎𝑥 + 𝑏 < 𝑘, Maám.
None, Maám.
D. Application
Teacher’s Activity Students’ Activity
If none, let us have practice exercises. You can
work with your seatmates and discuss. I will give
you 5 minutes.
Solve each equation and inequality.
1. | 𝑥 − 9| = 13
2. 7| 𝑥 + 5| − 18 = −4
3. |9𝑥 + 5| = |6𝑥|
4. |2𝑥 − 7| > 29
5. |3𝑥 + 12| < 42

4. 4 | 4
Are you all done? Who can answer them on the
board?
Let’s have ___, ___, ___, ___, and ___.
Are their answers correct? Did you also get the
correct answers?
Very good. Now are you ready for a quiz?
Please get a whole sheet of pad paper
(Raising hands)
Yes, Maám.
Yes, Maám.
E. Evaluation
Solve each equation and inequality.
1. | 𝑥| = 10
2. |4𝑥 + 3| − 2 = 5
3. |3𝑥 + 2| = |5𝑥 − 12|
4. |4𝑥 + 5| ≤ 97
5. |4𝑥 − 23| > 7
F. Assignment
1. Study word problems such as number problem, integer problem, age problem, and distance
problem.