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NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations - In this chapter, students will be introduced by a new concept 'Equation'. This topic not only builds knowledge of algebra for maths students of class 7 but also helps to develop analytical thinking. Solutions of NCERT Class 7 Maths chapter 4 Simple Equations have 4 exercises with 18 questions in them. The NCERT solutions for Maths chapter 4 Simple Equations class 7 also discuss some topic-wise questions.
The NCERT Solutions can be extremely helpful for the Class 7 Maths students to understand the basics of this chapter and to clear all their doubts easily. Students can use NCERT Solutions for Class 7 as worksheets to prepare for their CBSE final exams. Here you will get solutions to all four exercises of this NCERT chapter.
Balancing Equation:
LHS = RHS
(LHS ± a) = (RHS ± a)
(LHS × b) = (RHS × b)
(LHS ÷ c) = (RHS ÷ c)
Solution of an Equation: For a variable 'x', if LHS(x) = RHS(x), then 'x' is a solution.
Variable: Something that can vary, Its value is not fixed such as x, y, z, p, q, r, etc.
Equation: It is a mathematical statement that uses an equal sign(=) to show that the value of the expression to the left of the sign (LHS) is equal to the value of the expression to the right of the sign (RHS).
Interchangeability: If the LHS and RHS are interchanged, the equation remains the same.
Balanced equation: the value of LHS remains equal to the value of the RHS. If we,
Add the same number to both sides
Subtract the same number from both sides.
Multiply both sides by the same number.
Divide both sides by the same number.
Solution of an equation: The value of the variable for which the equation is satisfied ( for that variable, LHS = RHS ).
Transposing: Transposing of a number has the same effect as adding the same number to both sides or subtracting the same number from both sides of the equation.
Free download NCERT Solutions for Class 7 Maths Chapter 4 Simple Equation PDF for CBSE Exam.
NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Topic 4.3
Answer:
(i) Let y = 2 . We have :
(ii) Let y = 3 . We have :
(iii) Let y = 4 . We have :
(iv) Let y = 5 . We have :
(v) Let y = 6 . We have :
Hence 10y - 20 depends upon y.
Now, consider
Transpose - 20 to the RHS :
or
(ii) What is that number one third of which added to 5 gives 8?
Answer:
(i) Let the number be n.
Then according to the question, we have :
or
or
(ii) Let the number be x.
Then according to the question,
Answer:
Let the number of mangoes in the smaller box be n.
Then according to the question, we have :
or
or
Hence the number of mangoes in the smaller box is 12.
1. Complete the last column of the table.
Answer:
The table is shown below:-
2. Check whether the value given in the brackets is a solution to the given equation or not:
(a) n + 5 = 19 (n = 1)
(b) 7n + 5 = 19 (n = – 2)
(c) 7n + 5 = 19 (n = 2)
(d) 4p – 3 = 13 (p = 1)
(e) 4p – 3 = 13 (p = – 4)
(f) 4p – 3 = 13 (p = 0)
Answer:
(a) Put n = 1 in the equation, we have :
n + 5 = 15
or 1 + 5 = 15
or 6 15
Thus n = 1 is not a solution.
(b) Put n = - 2, we have :
7n + 5 = 19
or 7(-2) + 5 = - 14 + 5 = - 9 19.
So, n = - 2 is not a solution to the given equation.
(c) Put n = 2, we have :
7n + 5 = 19
or 7(2) + 5 = 14 + 5 = 19 = R.H.S
Thus n = 2 is the solution for the given equation.
(d) Put p = 1 , we have :
4p - 3 = 13
or 4(1) - 3 = 1 13 .
Thus p = 1 is not a solution.
(e) Put p = - 4 , we get :
4p - 3 = 13
or 4(1) - 3 = 1 13 .
Thus p = 1 is not a solution.
(f) Put p = 0 , we get :
4p - 3 = 13
or 4(0) - 3 = - 3 13 .
Thus p = 0 is not a solution.
3. Solve the following equations by trial and error method:
(i) 5p + 2 = 17 (ii) 3m – 14 = 4
Answer:
(i) Put p = 1,
We have :
Put p = 2,
We have :
Put p = 3,
we have :
Thus the solution is p = 3.
(ii) Put m = 4,
we have :
Put m = 5,
we have :
Now, put m = 6,
we have :
Thus m = 6 is the solution.
4. Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
(ii) 2 subtracted from y is 8.
(iii) Ten times a is 70.
(iv) The number b divided by 5 gives 6.
(v) Three-fourth of t is 15.
(vi) Seven times m plus 7 gets you 77.
(vii) One-fourth of a number x minus 4 gives 4.
(viii) If you take away 6 from 6 times y, you get 60.
(ix) If you add 3 to one-third of z, you get 30.
Answer:
The equations are given below :
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
5. Write the following equations in statement forms:
(i) p + 4 = 15
(ii) m – 7 = 3
(iii) 2m = 7
(iv) m /5 = 3
(v) 3 m/5 = 6
(vi) 3p + 4 = 25
(vii) 4p – 2 = 18
(viii) p /2 + 2 = 8
Answer:
(i) Add 4 to the number p, we get 15.
(ii) Subtract 7 from m to get 3.
(iii) Twice the number m is 7.
(iv) One-fifth of m is 3.
(v) Three-fifth of m is 6.
(vi) 4 is added to thrice the number p to get 25.
(vii) 2 is subtracted from the product of 4 times p to get 18.
(viii) When 2 is added to half of the number p, we get 8.
Answer:
(a) Let the Parmit's marbles be m.
Then according to the question we have :
or
(b) Let the age of Laxmi be y years.
Then we have :
or
(c) Let the lowest marks be l, then :
or
(d) Let the base angle of the triangle be b degree.
Then according to the question we have :
or
1. Give first the step you will use to separate the variable and then solve the equation:
(a) x – 1 = 0
(b) x + 1 = 0
(c) x – 1 = 5
(d) x + 6 = 2
(e) y – 4 = – 7
(f) y – 4 = 4
(g) y + 4 = 4
(h) y + 4 = – 4
Answer:
(a) Add 1 to both the sides, we have :
(b) Transpoing 1 to the RHS, we have :
(c) Transposing - 1 to the RHS, we have :
(d) Transposing 6 to the RHS, we get :
(e) Transposing - 4 to the RHS, we have :
(f) Transposing - 4 to the RHS, we get :
(g) Transposing 4 to the RHS, we get :
(h) Transposing 4 to the RHS, we get :
2. Give first the step you will use to separate the variable and then solve the equation:
(a) 3l = 42
(b) b / 2 = 6
(c) p /7 = 4
(d) 4x = 25
(e) 8y = 36
(f) z/ 3 = 5 /4
(g) a /5 =7/ 15
(h) 20t = – 10
Answer:
(a) Divide both sides by 3, we get :
(b) Multiply both sides by 2, we get :
(c) Multiply both sides by 7, we get :
(d) Divide both sides by 4, we get :
(e) Divide both sides by 8, we get :
(f) Multiply both sides by 3, we get :
(g) Multiply both sides by 5, we get :
(h) Divide both sides by 20, we get :
3. Give the steps you will use to separate the variable and then solve the equation:
(a) 3n – 2 = 46
(b) 5m + 7 = 17
(c) 20p / 3 = 40
(d) 3p/10 = 6
Answer:
(a) We have 3n – 2 = 46.
Transposing - 2 to the RHS, we have :
or
(b) We have 5m + 7 = 17
Transposing 7 to the RHS, we have :
or
(c) We have 20p / 3 = 40
Multiply both sides by :
or
(d) We have 3p/10 = 6
Multiply both sides by :
or
4. Solve the following equations:
(a) 10p = 100
(b) 10p + 10 = 100
(c) p /4 = 5
(d) – p/3 = 5
(e) 3 p/4 = 6
(f) 3s = –9
(g) 3s + 12 = 0
(h) 3s = 0
(i) 2q = 6
(j) 2q – 6 = 0
(k) 2q + 6 = 0
(l) 2q + 6 = 12
Answer:
(a) Divide both sides by 10, we get :
(b) Transposing 10 to the RHS, we get :
Now, dividing both sides by 10 gives :
(c) Multiplying both sides by 4, we have :
(d) Multiplying both sides by - 3 , we have :
(e) Multiplying both sides by , we have :
(f) Dividing both sides by 3, we have :
(g) Transposing 12 to the RHS and then dividing both sides by 3, we have :
(h) Dividing both sides by 3, we get :
(i) Dividing both sides by 2, we get :
(j) Transposing - 6 to the RHS and then dividing both sides by 2, we get :
(k) Transposing 6 to the RHS and then dividing both sides by 2, we get :
(l) Transposing 6 to the RHS and then dividing both sides by 2, we get :
1. Solve the following equations:
(b) 5t + 28 = 10
(c) a /5 + 3 = 2
(d) q/ 4 + 7 = 5
e) 5 x/2 = –5
(f)
(g) 7m + 19/2 = 13
(h) 6z + 10 = –2
(i)
(j)
Answer:
Transposing to the RHS :
(b) 5t + 28 = 10
Transposing 28 to the RHS and then dividing both sides by 5, we get :
(c) a /5 + 3 = 2
Transposing 3 to the RHS and multiplying both sides by 5, we get :
(d) q/ 4 + 7 = 5
Transposing 7 to the RHS and multiplying both sides by 4:
(e) 5 x/2 = – 5
Multiplying both sides by :
(f)
Multiplying both sides by :
(g) 7m + 19/2 = 13
Transposing to the RHS and then dividing both sides by 7 :
(h) 6z + 10 = –2
Transposing 10 to the RHS and then dividing both sides by 6, we get :
(i)
Multiplying both sides by ,
(j)
Transposing 5 to the RHS and then multiplying both sides by
2. Solve the following equations:
(a) 2(x + 4) = 12
(b) 3(n – 5) = 21
(c) 3(n – 5) = – 21
(d) – 4(2 + x) = 8
(e) 4(2 – x) = 8
Answer:
(a) We have:
2(x + 4) = 12
Dividing both sides by 2, we have :
Transposing 4 to the RHS, we get :
Thus
(b) We have:
3(n – 5) = 21
Dividing both sides by 3, we have :
Transposing - 5 to the RHS, we get :
Thus
(c) We have :
3(n – 5) = – 21
Dividing both sides by 3, we have :
Transposing - 5 to the RHS, we get :
Thus
(d) We have :
– 4(2 + x) = 8
Dividing both sides by - 4, we have :
Transposing 2 to the RHS, we get :
Thus
(e) We have :
4(2 - x) = 8
Dividing both sides by 4, we have :
Transposing x to the RHS and 2 to the LHS , we get :
Thus
Q3 Solve the following equations:
(a) 4 = 5(p – 2)
(b) – 4 = 5(p – 2)
(c) 16 = 4 + 3(t + 2)
(d) 4 + 5(p – 1) =34
(e) 0 = 16 + 4(m – 6)
Answer:
(a) 4 = 5(p – 2)
Dividing both sides by 5, we get :
or
(b) – 4 = 5(p – 2)
Dividing both sides by 5, we get :
or
(c) 16 = 4 + 3(t + 2)
Transposing 4 to the LHS and then dividing both sides by 3, we get :
or
or
(d) 4 + 5(p – 1) =34
Transposing 4 to the RHS and then dividing both sides by 5, we get :
or
or
(e) 0 = 16 + 4(m – 6)
Transposing 16 to the LHS, we get :
or
or
4. (a) Construct 3 equations starting with x = 2
(b) Construct 3 equations starting with x = – 2
Answer:
(a) The 3 required equations can be :
(b) The required equations are :
Answer:
Let the number in each case be n.
(a) According to the question:
or
or
(b) We have :
or
or
(c) The equation is :
or
or
(d) We have :
or
or
(e) The equation is :
or
or
(f) We have :
or
or
(g) We have :
or
or
Answer:
(a) Let the lowest score be l.
Then according to the question, we have :
or
or
Thus the lowest marks are 40.
(b) Let the base angle of a triangle is .
Then according to the question, we get :
or
or
or
(c) Let the runs scored by Rahul is x. Then runs by Sachin is 2x.
Further, it is given that their runs fell two short of a double century.
Thus we have :
or
or .
Hence runs by Rahul is 66 and the runs scored by Sachin is 132.
Answer:
(a) Let the number of Parmit's marble be n.
Then according to question, we have :
or
or
or
(b) Let the age of Laxmi be x.
Then according to the question, we have :
or
or
(c) Let the number of fruit trees planted be z.
Then according to the question, we have :
or
or
Answer:
Let the number be x.
According to the question the equation is :
or
or
or
Hence the number is 30.
NCERT Class 7 Maths book chapter 4 Simple Equations begin with a fun game 'mind-reading' and introduce the concept of the equation. So what is an equation? It is a condition on the variable such that two expressions in the variable should have equal value. The value of the variable for which an equation is satisfied is called the solution of the equation. In the equation, there is always an equality(=) sign. The equality sign shows that the value of the expression to the left-hand side (LHS) of the equality sign is equal to the value of the expression to the right-hand side (RHS) of the equality sign. For example, the equation 3x+ 7 =2x - 35 has the expression (3x + 7) on the left of the equality sign and (2x - 35) on the right of the equality sign. But it is not an equation if there is a sign other than the equality sign. For example, 3x + 5 > 75 is not an equation.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | Simple Equations |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | |
Chapter 8 | Comparing quantities |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 | Visualising Solid Shapes |
As far as the subject Mathematics is concerned, the practising problem is important to score well in exams. It is important to know how to apply the concepts studied in an application-level problem. This is achieved through practice and the CBSE NCERT solutions for Class 7 Maths chapter 4 Simple Equations help for the same. The solutions of NCERT Class 7 Maths chapter 4 Simple Equations are helpful in solving homework problems.
Also Check NCERT Books and NCERT Syllabus here:
According to chapter 4 maths class 7, A simple equation is a mathematical statement that shows that two expressions are equal. It has an equal sign (=) between the two sides.
To solve a simple equation, aim to isolate the variable (usually represented by a letter) on one side of the equation.
Perform the same operations on both sides of the equation to keep it balanced. This maintains the equality of the expressions.
The goal is to find the value of the variable that satisfies the equation. This value will make both sides of the equation equal.
Also Practice chapter 4 maths class 7 solutions to command the concepts.
According to class 7th chapter 4 maths, an extraneous solution is a solution that appears to work in the process of solving an equation but doesn't satisfy the original equation.
They often arise from operations that introduce restrictions, like division by zero or square roots of negative numbers.
To avoid extraneous solutions, always check the solutions you find by substituting them back into the original equation. If the substituted value doesn't satisfy the equation, it's not a valid solution.
Practice class 7th chapter 4 maths solutions to get in-depth understanding of the concepts.
Here is the topics are covered in NCERT solution Maths Class 7 chapter 4
Also To get command on the concepts, practice class 7 chapter 4 maths solutions.
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Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.
Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.
A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.
A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.
A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.
In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.
Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.
For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.
In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.
Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.
Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.
Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning).
Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian.
The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack
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