This is the Mathematics 7 Quarter 2 Module 8 self-learning module (SLM), Algebraic Expressions, Linear Equations and Inequalities, prepared by DepEd Region XII under the Alternative Delivery Mode (First Edition, 2020). It is for Grade 7 learners studying at home or in class, and for the teachers and parents who guide them. After working through it, learners should be able to tell a linear equation from a linear inequality in one variable and give examples of each.
What learners will learn
The module states that, after going through it, learners are expected to:
- define and differentiate linear equation and inequality in one variable; and
- illustrate linear equation and inequality in one variable.
Lessons in this module
The module has one lesson.
- Lesson 1: Algebraic Expressions, Equations and Inequalities. It reviews expressions and equations, introduces inequalities, and then explains linear equations and linear inequalities in one variable, including their standard forms and symbols.
Key ideas: expressions, equations, and inequalities
The lesson begins with a review of the basic terms.
- Algebraic expression: made up of constants and variables, joined by operations such as addition and subtraction. Examples: 5a – 75, 2y + 5y, 3m – 4.
- Variable: usually a letter. Its value can vary.
- Constant: a number, letter, or symbol whose value is fixed.
- Equation: a statement that two numbers or two algebraic expressions are equal. Examples: 5m + 20 = 10, 6b – 23 = 27, 4p – 29 = -11.
- Open sentence: an equation with a variable. It can be true or false depending on the value of the variable. The value that makes it true is the solution.
- Closed sentence: a statement with no variables, such as 1 + 2 = 3 or 10 – 2 = 8.
- Inequality: a statement that relates two quantities using an inequality symbol such as <, >, ≤, or ≥. Examples: z ≥ 7, n + 9 > 7, k – 9 < 18.
A quick way to sort them: an expression has no equal sign or inequality symbol (8p – 90, 3c + 9). An equation uses “=” (4a – 11 = 18). An inequality uses an inequality symbol (3x > 7).
Key ideas: linear equations and inequalities in one variable
Linear equation
An equation is linear when its highest degree is one. For example, 8x + 4 = 12 is linear. 2xy = 10 and 5ab + 10 = 20 are not linear.
A linear equation in one variable has only one variable, and that variable has a power of 1. Its standard form is:
ax + b = c, where a, b, and c are real numbers and a ≠ 0.
The module’s examples include 3x = 1, 4x + 9 = -11, x = 7, and 3z + 4 = 12 – z.
Linear inequality
A linear inequality in one variable also has one variable with an exponent of 1. It compares the two sides with an inequality symbol, which means the two sides are not equal. Its standard form is:
ax + b > c, where a, b, and c are real numbers and a ≠ 0.
The module’s examples include 2x + 4 < 2, x > -2, x ≥ 0, and 2(x – 8) < 10.
Inequality symbols
| Symbol | Meaning |
|---|---|
| < | less than |
| > | greater than |
| ≤ | less than or equal to, at most |
| ≥ | greater than or equal to, at least |
| ≠ | not equal to |
How they are alike and different
According to the answer key, linear equations and linear inequalities both have one variable whose highest exponent is 1. The difference is the symbol: an equation uses the equal sign, and an inequality uses an inequality symbol.
How to use this module
The module follows the usual SLM parts, in this order:
- What I Know: a 15-item multiple-choice pretest. It shows what you already know.
- What’s In: a review of expressions and equations, with a two-column comparison exercise.
- What’s New: sort nine items into expressions, equations, and inequalities.
- What is It: the main discussion of linear equations and inequalities.
- What’s More: label 10 items as an equation or an inequality.
- What I Have Learned: fill in a compare-and-contrast chart.
- What I Can Do: check whether each of 10 items is an equation or an inequality.
- Assessment: a 15-item multiple-choice post-test.
- Additional Activities: model inequalities with tiles. Green and red circles stand for positive and negative 1. Green and red squares stand for positive and negative x.
An answer key for every part is at the end of the module.
- Learners: Write your answers on a separate sheet of paper and do not mark the module. Check your work with the answer key only after you answer, and be honest when you use it.
- Parents and facilitators: The module includes notes on how to support home-based learning. Encourage your child to ask the teacher when a task is unclear.
- Teachers: The pretest and post-test cover the same skills, so you can compare the two scores to see how much each learner has learned.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 7 Mathematics, Quarter 2. It is Module 8 of that quarter.
Does the module have an answer key?
Yes. The answer key at the end covers the pretest, every activity, the post-test, and the additional activities.
What is the difference between a linear equation and a linear inequality in one variable?
Both have one variable with a highest exponent of 1. A linear equation uses the equal sign, as in ax + b = c. A linear inequality uses a symbol such as <, >, ≤, ≥, or ≠, as in ax + b > c.
What is the standard form of a linear equation in one variable?
The module gives it as ax + b = c, where a, b, and c are real numbers and a is not 0.
How many lessons are in this module?
There is one lesson: Algebraic Expressions, Equations and Inequalities.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics 7 Quarter 2 – Module 8: Algebraic Expressions, Linear Equations and Inequalities
Mathematics 7 Quarter 2 – Module 8: Algebraic Expressions, Linear Equations and Inequalities
[illustration: students and a teacher studying outdoors and at a desk, with a globe and a lantern]
CO_Q2_Math7_Module 8
Mathematics – Grade 7 Alternative Delivery Mode Quarter 2 – Module 8: Algebraic Expressions, Linear Equations and Inequalities First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Printed in the Philippines by _____
Department of Education – Region XII Office Address: Regional Center, Brgy. Carpenter Hill, City of Koronadal Telefax: (083) 2288825/ (083) 2281893 E-mail Address: region12@deped.gov.ph
Development Team of the Module
Writers: Ana Cristy P. Mercado, Eliza B. Aguelo Editor: Venus Jane E. Rosete Reviewer: Reynaldo C. Tagala Illustrator: Ian Caesar E. Frondoza Layout Artist: Maylene F. Grigana Management Team: Allan G. Farnazo, CESO IV – Regional Director Gilbert B. Barrera – CLMD Chief Arturo D.Tingson Jr. -Regional EPS In Charge of LRMS Peter Van C. Ang-ug- Regional ADM Coordinator Donna S. Panes – CID Chief Elizabeth G. Torres – Division EPS In Charge of LRMS Judith B. Alba – Division ADM Coordinator
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
[illustration: target with arrow]
What I Need to Know
This module was designed and written with you in mind. It is here to help you master the Algebraic Expressions, Linear Equations and Inequalities. The scope of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.
The module is comprised of only one lesson:
- Algebraic Expressions, Linear Equations and Inequalities
After going through this module, you are expected to:
- define and differentiate linear equation and inequality in one variable; and
- illustrate linear equation and inequality in one variable.
What I Know
[illustration: pencil icon]
Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper.
It is a mathematical sentence which states that the two expressions are unequal.
- A. Equation
- B. Equivalent
- C. Expression
- D. Inequality
It is a statement in which two expressions, at least one containing the variable are equal.
- A. Equation
- B. Equivalent
- C. Expression
- D. Inequality
Complete the statement: “When the highest power of the variable of an equation is 1, the equation is _____.”
- A. Equivalent
- B. Indirect
- C. Inequality
- D. Linear
All of the following are linear inequality, EXCEPT:
- A. x ≤ 7
- B. x + 2 < 1
- C. 2x – 4 ≤ 3
- D. 4x+7 = 12
All of the following are linear equations, EXCEPT:
- A. 12 + y ≠ 10
- B. 3x – 6 = 9
- C. 7(x- 3) = 42
- D. 3x + 9 = 27
The symbol “=” is used to indicate _____.
- A. Equation
- B. Equality
- C. Inequality
- D. Equivalent
The symbol “<, >, ≤, ≥, ≠” is used to indicate _____.
- A. Equation
- B. Equality
- C. Inequality
- D. Equivalent
Which of the following is a linear equation in one variable?
- A. 3x – 4 < 2
- B. 5x – 4 = 12
- C. 8x – 6 = 2y
- D. 10x + 30
How many variables are there in equation 5x + 2x = 10x – 20?
- A. 0
- B. 1
- C. 2
- D. 3
Which expression represents the phrase “a number x less the number y”?
- A. x < y
- B. y – a
- C. y < x
- D. x – y
Express 2 (x + 3) = 25 in the standard form of linear equation ax + b = c.
- A. 2x + 6 = 25
- B. 2x + 3 = – 25
- C. 2x – 6 = – 25
- D. 2x – 3 = 25
Which of the following is a linear inequality in one variable?
- A. 2x + 4 < 2
- B. 3x >y+1
- C. 22x – 1 = 0
- D. 4x + 9 = -11
A part of an algebraic expression separated by the “+” and “-” signs.
- A. Coefficient
- B. Constant
- C. Term
- D. Variables
What is the simplified form of 7 (x – 2) = 5x – 10?
- A. 7x – 14 =10
- B. 2x – 14 = 10
- C. 2x – 14 = -10
- D. 7x-14 = 5x -10
What is the simplified form of 2(x – 8) < 10?
- A. 2x – 16 = 10
- B. x – 4 < 5
- C. 2x – 16 < 10
- D. 2x – 16 >10
Lesson 1: Algebraic Expressions, Equations and Inequalities
In this lesson, you will learn the definition and differences between linear equation and inequalities in one variable.
What’s In
[illustration: puzzle pieces icon]
Before going to the actual topic, let’s review!
Algebraic Expressions are expressions made up of constant and variable, along with algebraic operations such as addition and subtraction. A variable, usually represented by a letter, takes a quantity or value that may vary. A constant is a number, letter, or symbol whose value is fixed.
Examples:
5a – 75 2y + 5y 3m – 4
An equation is a mathematical statement which expresses that two numbers or two algebraic expressions are equal. An equation that contains a variable is an open sentence which can be true or false depending on the value of the variable. The value of the variable that makes the equation true is a solution of the equation.
Examples:
5m + 20 = 10 6b – 23 = 27 4p – 29 = -11
A closed sentence is a mathematical statement containing no variables.
Examples:
1 + 2 = 3 2 (6) = 12 10 – 2 = 8
Do the exercise below.
Exercise: Shown below are two columns, A and B. Column A contains expression while Column B contains equations. Observe and compare the items under each column then answer the questions that follow.
| Column A: Mathematical Expressions | Column B: Mathematical Equations |
|---|---|
| x + 2 | x + 2 = 5 |
| 2x – 5 | 4 = 2x – 5 |
| x + 4bc | x = 2 |
| 7x – 7 | 7 = 3 – x |
| _____ | _____ |
How are items in column B different from Column A?
What symbol is common in all items of Column B?
Write at least two other examples on the space provided below each column.
What’s New
[illustration: sprouting seedling icon]
Previously, you just have learned about expression and equation. Now, let’s try to review about inequalities.
An inequality is any mathematical statement relating two quantities using an inequality symbol such as <, >, ≤ or ≥.
Examples:
z ≥ 7 n + 9 > 7 k – 9 < 18
Now, let’s try this!
Group the following to which they belong.
2x – 2 < 6x – 5 7b + 5 = – 9 8p – 90 6y + 1 ≥ 3 3c + 9 4a – 11 = 18 a + 2 = 22 68+ 2y 3x > 7
| Expression | Equation | Inequalities |
|---|---|---|
Answer the following questions:
- How many groups are there?
- What symbols did you observe in each group?
- How many variables are there in each expression?
What is It
Linear Equation is defined as one degree equation or the highest degree of an equation is one. To determine a linear equation, look at the highest degree of an equation. If the highest degree of the equation is one, then it is a linear equation. If the highest degree of the equation is not one, then it is not a linear equation.
Examples of linear equation:
4x + 3y = 8 8x + 4 = 12 3a + 4b – 5c = 10d
Examples of not linear equation:
2xy = 10 3x + 4xy – 6z = 20 5ab + 10 = 20
Linear Equation in One Variable
A linear equation in one variable is an equation has a maximum of one variable of order 1, which is expressed in the form ax + b = c where a and b are integers and x is a variable and has only one solution. The symbol “=” is used to indicate equality.
[chart: diagram; Standard Form of Linear Equation in One Variable]
Standard Form of Linear Equation in One Variable
The standard form of linear equations in one variable is represented as:
left side ← ax + b = c → right side
↓ Equal sign
where a,b, and c are real numbers and a ≠ 0.
The following are some examples of linear equations in one variable.
3x = 1 22x – 1 = 0 4x + 9 = -11
5 (y – 2) = 5y – 10 x = 7 3z + 4 = 12 – z
Linear Inequality in One Variable
A linear inequality is a statement involving one variable which exponent is 1,where inequality rather than equality is the center of focus. The word “inequality” indicates that the expression on the left and right sides of inequality are not equal.
| Inequality Symbols | |
|---|---|
| < | less than |
| > | greater than |
| ≤ | less than, equal to or at most |
| ≥ | greater than or equal to, at least |
| ≠ | not equal to |
[chart: diagram; Standard Form Linear Inequality in One Variable]
Standard Form Linear Inequality in One Variable
Is an inequality which can be put into the form
left side ← ax + b > c → right side
↓ Inequality sign
where a, b and c are real numbers and a≠0.
The following are some examples of linear inequalities in one variable.
2x + 4 < 2 x > – 2 x ≥ 0
2x – 2 < 6x – 5 6x + 1 ≥ 3 (x – 5) 2(x – 8) < 10
What’s More
Identify which of the following expressions is an equation or an inequality. Write your answer on a separate sheet of paper. Do not copy the expressions anymore.
_____ 1) 7x + 2 = – 19
_____ 2) 3(x+ 4) = 21
_____ 3) 5x – 4 < 21
_____ 4) 3x – 9 > 5x – 3
_____ 5) 3 (x- 3) = 4 (2x + 1)
_____ 6) 7x – 2 = 8 – x
_____ 7) 2x – 6 ≥ 0
_____ 8) 2 (x – 1) + 2 (3x – 1) ≤ 0
_____ 9) 4 + 3x = 2 – 2x
_____ 10) 8 – 2x = 5 – 4x
What I Have Learned
To check your understanding of the linear equation and inequality, accomplish this compare and contrast chart. You can provide your own examples in establishing how are they alike and how are they different.
[chart: graphic organizer; Compare and Contrast Chart Graphic Organizer]
Compare and Contrast Chart Graphic Organizer
Linear Equation | Linear Inequality
How are they alike?
How are they different?
Linear Equation | Linear Inequality
What I Can Do
Complete the following table by placing a check mark (✔) on the cells that illustrate linear equation or inequality in one variable.
| Equation | Inequality | |
|---|---|---|
| 1.) 4x – 5 = 3 | ||
| 2.) x – 6x > 0 | ||
| 3.) 10x = x + 3 | ||
| 4.) 3x – 2x = 1 | ||
| 5.) 15 + 2x < 8 | ||
| 6.) 15y = y – 3 | ||
| 7.) 5p > 8 + 2 | ||
| 8.) 8x – 12 = 4 | ||
| 9.) -2y + 9y > 0 | ||
| 10.) 7y + 2 < 50 |
Assessment
Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.
It is a combination of numbers, operations and variables.
- A. Equation
- B. Equivalent
- C. Expression
- D. Inequality
It is a statement which expresses that two numbers or algebraic expressions are equal.
- A. Equation
- B. Equivalent
- C. Inequality
- D. Linear
It is any mathematical statement relating two quantities using the symbol >, <, ≤ or ≥.
- A. Equation
- B. Equality
- C. Inequality
- D. Equivalent
The symbol “=” is used to indicate _____.
- A. Equation
- B. Expression
- C. Inequality
- D. Sign
Complete the statement: “When the highest power of the variable of an equation in one variable is 1, the equation is _____”.
- A. Indirect
- B. Inequality
- C. Linear
- D. Solution
All of the following are linear inequality, EXCEPT:
- A. x ≤ 0
- B. x = 2
- C. x – 4 ≤ 3
- D. x – 4 ≠ 12
All of the following are linear equation, EXCEPT:
- A. 5 + y ≠ 10
- B. 3x – 6 = 21
- C. 3(x- 3) = 81
- D. 7x + 8 = 72
Which mathematical equation has one variable?
- A. x – 5y = 5
- B. 12 + y ≠ 10
- C. y + 8 =10
- D. 5x – 1 = 2y+4
Which mathematical inequality has one variable?
- A. x – 5 = 5
- B. 12 + y = 10
- C. y + 8 ≠2y +10
- D. 5x – 1 < 2y+4
Which of the following is a linear equation in one variable?
- A. 3x – 4 < 2
- B. 5x – 4 > 12
- C. 8x > 1
- D. 10x = 30
Which of the following is a linear inequality in one variable?
- A. 5x ≥ 4
- B. 3x – 6
- C. 7(x- 3) = 42
- D. 3x + 9 = 27
Which of the following is a linear equation in one variable?
- A. 3x + 7 = 16
- B. -2x + 1 ≥ 21
- C. 2x + 3 > 4
- D. 3x + 7y = 6
Which of the following is a linear inequality in one variable?
- A. 2x + 4 < 2
- B. 3x =1
- C. 5y < x
- D. 4x + 9 = -11
Write the simplified form of 3(x – 2) = 2 (x – 2).
- A. 3x – 6 =4x -4
- B. 3x = 10
- C. x – 6 = -4
- D. x-6 > 4
Write the simplified form of 2(x +9) < 10.
- A. 2x – 18 = 10
- B. x – 18 < 10
- C. 2x +18 < 10
- D. 2x + 18 =10
Additional Activities
Illustrate each linear equations and inequalities in one variable by modeling each expression. An example is provided for you.
Legend:
[illustration: green circle] – represent constant 1 (positive)
[illustration: red circle] – represent constant 1 (negative)
[illustration: green square] – represent variable x (positive)
[illustration: red square] – represent variable x (negative)
| Expression | Illustration |
|---|---|
| 1. 3x – 5 < 2 | [illustration: three green squares, five red circles, “<“, two green circles] |
| 2. x + 3 > 1 | |
| 3. 3x ≥ 6 | |
| 4. 2 – 3x > x – 3 | |
| 5. 2x – 3 ≤ 5 |
Answer Key
[transcriber’s note: the answer key grid is printed upside down on the page; the parts are transcribed below in the order of the answer key, not in the order they appear on the printed grid]
What I Know
- D
- A
- D
- D
- A
- B
- C
- B
- B
- D
- A
- A
- C
- C
- C
What’s In
- Column A consists of mathematical phrases while Column B consists of two mathematical sentences.
- The equal sign “=”
- Answer may vary.
What’s New
- Three groups.
Group of Expression: 8p – 90, 3c + 9, 68 + 2y
Group of Equation: 4a – 11 = 18, 7b + 5 = -9, a + 2 = 22
Group of Inequality: 2x – 2 < 6x – 5, 6y + 1 ≥ 3, 3x > 7
There are three groups. Expression used variable and constant. Linear equation used equal sign while linear inequality used inequality symbol.
One variable.
What’s More
- Equation
- Equation
- Inequality
- Inequality
- Equation
- Equation
- Inequality
- Inequality
- Equation
- Equation
What I Have Learned
- How are they alike? They have one variable with the highest exponent of 1.
- How are they different? Linear equation used equality symbol while linear inequality used inequality symbol.
What I Can Do
- Equation
- Inequality
- Equation
- Equation
- Inequality
- Equation
- Inequality
- Equation
- Inequality
- Inequality
Assessment
- C
- A
- C
- A
- C
- B
- A
- C
- C
- D
- A
- A
- A
- C
- C
Additional Activities
[transcriber’s note: the box is printed upside down, and the shapes are read as they appear in the image, left to right; the counts and symbols marked [?] are uncertain]
- [illustration: two green circles, “>”, five red circles, “<“, three green squares] [?]
- [illustration: one green circle, “>”, three green circles, one green square] [?]
- [illustration: five green circles, “≥”, three green squares] [?]
- [illustration: three red squares, “>”, three red squares, two green circles] [?]
- [illustration: five green circles, “≤”, three red circles, two green squares] [?]
References
- K TO 12 GRADE 7 LEARNING MODULE IN MATHEMATICS (Q1 – Q2). (2014, March 11). Retrieved from https://www.slideshare.net/lhoralight/k to 12grade 7 learning material in mathematics q1q2
- Slideplayer.com published by Anthony Parsons Academia .ed
- Learning Module Mathematics G7/Q2 Private Education Assistance Committee
- Grade 7 Mathematics – Patterns and Practicalities, Updated Edition, pp. 278-282; 296-298.
For inquiries or feedback, please write or call:
Department of Education – Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
Leave a Reply