# Chapter 3 – Algebra

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

In mathematics, algebra is the branch that revolves around solving certain mathematical equations in order to derive unknown quantities. The variables in algebra can be used to equate known quantities or constant values to solve for the unknown value that is required as the answer. We usually denote this unknown variable with ‘x’ or ‘y’ conventionally.

#### Introduction To Algebraic Expressions

We use algebraic formulas in our daily lives to find out the distance, volume of containers and also to find out prices of goods and commodities in large numbers. Algebra is helpful in defining a mathematical equation that can then form relationships with other values and entities to ultimately give you a solvable equation.

Some of the main topics in the NCERT syllabus for algebra include coming under algebra exponents, simplification, linear equations, linear inequalities, quadratic equations, polynomials, to name a few. As we know, algebra is the branch of mathematics that is based on unknown values called variables. This integral concept of algebra is expressed via equations that follow the various rules to perform arithmetic operations in order to solve for the unknown variable.

#### Addition And Subtraction Of Algebraic Expressions

Addition and subtraction of two or more algebraic expressions is relatively easy. It is quite similar to the arithmetic formats. It is also easy to generate algebraic expressions in the same way.

1. Write down the algebraic expressions given to you one below the other wherein the variables that are matching in the two equations are written directly below each other.
2. Then we merely add the constant coefficients to each other arithmetically to arrive at the value.
3. We then write the answer with the variable and the new value of the constant after addition to arrive at the result required.

Example:

Add 5x – 12y and y – 3x.

Solution:

For adding these 2 given algebraic expressions we write as follows:

5x – 12y
-3x + y
_______

Subtraction is a little different from the basic arithmetic subtraction. The steps for the same are mentioned below:

1. Write down the terms containing the same variables below one another.
2. Note the subtracted value and the expression from which the values are to be subtracted. This order of expressions is integral.
3. Then merely change the arithmetical operator associated with each term from the expression to be subtracted.
4. Then perform mere arithmetic subtraction to arrive at the answer you require.

Example:

Subtract x + y from 15y – 4x

Solution:

Write down the two given equations as follows:

-4x +15y
+x + y
(-)  (-)
________

#### Linear Equations In One Variable

Any algebraic expression that is written in the form of an equation in the generic form of ax + b =0 is called a simple linear equation or a linear equation in one variable. In this case, the variable is ‘x’ and the coefficient associated with this variable is ‘a’ which is usually a numerical value. This form of a linear equation in one variable has only one possible solution.

The standard form of simple linear equations in one variable is represented as:

ax + b = 0

Where ‘a’ and ‘b’ can be any real number which is not equal to zero.

For solving an equation having only one variable, the following basic steps are required to be closely followed:

• Take an LCM of both sides if there are any decimals or fractions in the expression given.
• Simplify both sides of the equation, change the arithmetical operator when moving from one side to the other.
• Isolate the variable to express in the form of ax + b =0 and then solve for x.

Here are a few Problems based on simple equations:

Example 1:

Solve for x: 13x + 39 = 0

Solution:

To simplify the given equation we do it as follows:

> 13x = -39

> x = -39/13

Thus, x from the above equation is equal to -3.

Example 2:

Solve for x: 10x + 12 = 21 – 3x

Solution:

To solve the given equation we need to write it in the form of ax +b = 0. We do so as follows:

> 10x + 12 = 21 – 3x

> (10x + 3x) + (12 -21) = 0

> 13x – 9 = 0

> 13x = 9

> x = 9/13 which is the required answer.

#### Linear Inequalities

Linear inequalities are certain types of algebraic expressions where any two values are compared to each other using inequality operators such as ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be arithmetical or algebraic or a mix of both.

The main symbols used in inequalities are:

• < (less than)
• > (greater than)
• ≤ (less than or equal to)
• ≥ (greater than or equal to)
• ≠ (not equal to)

#### Conclusion

In algebra, the idea to solve for acquiring the values for the unknown variables. It contains various topics such as linear equations in one variable, simple linear equations, linear inequalities, addition and subtraction of linear equations, etc. It is one of the most conceptual branches in maths and is easy to grasp if the basic concepts are clear.

#### FAQs

1. What is algebra in mathematics?
In mathematics, algebra is the branch that revolves around solving certain mathematical equations in order to derive unknown quantities. The variables in algebra can be used to equate known quantities or constant values to solve for the unknown value that is required as the answer.
2. What do you mean by linear equations?
Any algebraic expression that is written in the form of an equation in the generic form of ax + b =0 is called a simple linear equation or a linear equation in one variable. This form of a linear equation in one variable has only one possible solution.

3. What are linear inequalities?
Linear inequalities are certain types of algebraic expressions where any two values are compared to each other using inequality operators such as ‘<’, ‘>’, ‘≤’ or ‘≥’. These values could be numerical or algebraic or a combination of both.

4. What are the various types of expressions in algebra?
There are five main types of algebraic expressions. These are monomial or polynomial equations, exponential equations, trigonometric equations, logarithmic equations and rational equations.

5. How to solve a linear equation in one variable?
For solving a linear equation having only one variable, take an LCM of both sides if there are any decimals or fractions in the expression given. Then, simplify both sides of the equation, change the arithmetical operator when moving from one side to the other. Finally, isolate the variable to express in the form of ax + b =0 and then solve for x.

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### High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
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• Electrons and Photons
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• Force And Laws Of Motion
• Gravitation
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• Magnetism and Matter
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• Motion in a plane
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• Wave Optics
• Waves
• Work, Power and Energy

### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
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• Chemical Bonding and Molecular Structures
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• Chemistry of p-Block elements
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• Study of Compounds
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• The d-block and f-block elements
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• The p-Block Elements
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### High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
• Animal Kingdom
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• Biodiversity and Conservation
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• Biological Classification
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• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
• Cell Reproduction
• Cellular Respiration
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• Circulation
• Control And Coordination
• Crop Improvement
• Digestion and Absorption
• Diversity In Living Organisms
• Ecosystem
• Environmental Issues
• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
• Heredity And Evolution
• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
• Human Eye And Colourful World
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• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
• Kingdom Monera
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• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
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• Reproductive Health
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• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
• Hydrogen
• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time