Solution of a Linear Equation - eAge Tutor

English Guide: Practical Tips for Better English Communication

article thumbnailA rich vocabulary is an important indicator of a person’s command over the English language. That is one of the reasons why we keep offering tips regularly on how to improve your English vocabulary. However, building one’s vocabulary requires sustained effort to discover and add new words that can be used effectively in your communication. The process of enriching one’s vocabulary can be simplified into 4 key steps: read a lot of good English...
article thumbnailThe last two decades have been hugely transformational as digital technologies have disrupted every walk of life. This will only continue in the new decade, as machine learning, deep learning and artificial intelligence (AI) begin to play an integral part in our workplaces. As a result, workplaces will require very different skillsets than they needed until now. If you are a youngster looking for rapid career development in this new decade,...
article thumbnailIf you are planning to study, work or even immigrate to any western country (Australia, New Zealand, US, Canada, UK – to name a few), you will most likely be required to get a good IELTS score to get the requisite entry visa. Typically, this means that you should get a score of band 7 or higher to maximise the chances of getting the visa approval. The IELTS score contributes significant points to the points-system used by many countries for...
article thumbnailRecently, the former Union Minister and former top UN diplomat Mr.Shashi Tharoor was asked the secret of his exceptional English vocabulary. While he joked initially, he then gave the secret of his amazing and enviable vocabulary: Reading. Yes, the open secret to a strong and deep English vocabulary is as simple as that- a lot of reading of good English books.         Mr.Tharoor dispelled the notion that he moves around carrying an English dictionary....
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article thumbnailIt is never a pleasant task to call up the customer service of one of your service providers and complain about any issue you may have encountered, whether it is a faulty bill or inadequate service you have received. Nevertheless, making unpleasant telephone conversations to lodge a complaint is a part of life that one must be prepared for. How you go about making this conversation can go a long way in determining whether you get the desired...
article thumbnail  Let us say that your current English speaking skills aren’t great. You aren’t very confident of being able to communicate confidently and effectively in English with anyone, be it a small group or a large one. However, you are very determined to improve your spoken English skills rapidly and prove to yourself that you can do it, while making a good impression on those around you. Taking up an English speaking course is obviously one way to...
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article thumbnailEnglish language has plenty of words that seem very similar but mean very different. It is quite easy to ignore the subtle difference in the words themselves and consider them to mean the same thing. This results in incorrect usage of the words when writing or speaking in English, which may confuse the listener or create a negative impression about your English Communication skills. Let’s focus on two words, improve and improvise; the former is a...
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article thumbnail  We all have encountered situations wherein there were unavoidable or unforeseen circumstances because of which we had to extend our leave. For example, sickness, family issues, marriage etc. Now here comes the uncomfortable question – how to ask the boss for a leave extension. Quite tricky, huh?     When you are already on leave and then you have to request for extension of leave, it should be done in such a way that it is granted without much...
article thumbnailA few months back, a video of a job prospect venting out his frustrations on having to speak in English at job interviews, went viral. The protagonist of the video, a youngster, who could speak English fluently was angry that he was always asked to speak in English, and he let out his frustration with a series of expletives in Hindi. The fact that the video went viral and was shared by a large audience in the country, especially among...
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article thumbnailIndia is undergoing a digital revolution. The country has embarked on the ‘Digital India’ movement that has been officially promoted by the Indian government. It is therefore not surprising to see a jump in career opportunities in the field of digital marketing, especially search engine marketing (SEM). This field attracts a lot of freshers and young job aspirants. Having good English skills will enable a person to take advantage of the growing...
article thumbnailGood manners will open doors that the best education cannot.” Etiquette is the science of living. It embraces everything.People all over the world are judged, liked, disliked, remembered or looked down with contempt based on their manners. Good manners speak a lot about your personality.       It is imperative that you display your best behaviour when you are in a public place especially when eating out.  When you walk into a restaurant you don’t want to...
article thumbnailGood teamwork is essential not only for the growth of any organisation but also for the personal growth of individuals in the organisation. An essential component of achieving good team bonding is when team members express positive thoughts about fellow team members to them directly.  Sincere compliments and praise go a long way in making a person feel good and feel motivated to perform better for the team and the organisation.     There are a...
article thumbnailAt the outset, let us state that we hope you never have to apply for a compassionate leave. However, the reality is that most of us, at some stage of our life, end up having to request for such leaves. This article is written to specifically help you in case of such an eventuality.     Before we get into the mechanics of applying for compassionate leave, let us first understand what is compassionate leave. It is leave granted to an employee upon...

Solution of a Linear Equation


Solving a linear equation means determining it roots.

Three methods of solving a linear equation:

a) Trial and Error method.

b) Systematic method.

c) Transposition method.

Let’s go through each of the method one by one.

Trial and Error method

In this method, we often make a guess of the root of the equation. We find the values of L.H.S. and R.H.S. of the given equation for different values of the variable. The value of the variable for which L.H.S. = R.H.S. is the root of the equation.

Example: Solve x + 7 = 10 by the trial and error method.

We first evaluate the L.H.S. and R.H.S. of the given equation for some values of x and continue to give new values till the L.H.S. becomes equal to the R.H.S.


Clearly, L.H.S. = R.H.S. for x = 3. Hence, x = 3 is the solution of given equation.

Systematic method

In this method, we solve the equation by using the following rules:
Rule 1 – Same quantity (number) can be added to both sides of an equation without changing the equality.
Rule 2 – Same quantity (number) can be subtracted from both sides of an equation without changing the equality.
Rule 3 – Both sides of an equation may be multiplied by the same non – zero number without changing the equality.
Rule 4 - Both sides of an equation may be divided by the same non – zero number without changing the equality.

Example: Solve the equation: X/5 + 11 = 1/15.
We have, X/5 + 11 = 1/15
X/5 + 11 – 11 = 1/15 -11
X/5 = 1/15 – 11
X/5 = (1 – 165)/15
X/5 = -164/15
5 x X/5 = 5 x -164/15
X = -164/3
Thus, X = -164/3 is the solution of the given equation.

Transposition method

The transposition method involves the following equation:
Step 1 – Obtain the linear equation.
Step 2 – Identify the variable (unknown quantity) and constants (numerals).
Step 3 – Simplify the L.H.S. and R.H.S. to their simplest forms by removing brackets.
Step 4 – Transpose all terms containing variable on L.H.S. and constant terms on R.H.S. Note that the sign of the terms will change in shifting them from L.H.S. to R.H.S. and vice versa.
Step 5 – Simplify L.H.S. and R.H.S. in the simplest form so that each side contains just one term.
Step 6 – Solve the equation obtained in Step 5 by dividing both sides by the coefficient of variable on L.H.S.
Example:  Solve: X/2 – 1/5 = X/3 + 1/4
We have, X/2 – 1/5 = X/3 + 1/4
The denominators on two sides are 2, 5, 3 and 4.Their L.C.M. is 60.
Multiplying both sides of the given equation by 60, we get
60 (X/2 – 1/5) = 60 (x/3 +1/4)
60 x X/2 – 60 x 1/5 = 60 x X/3 + 60 x 1/4
30X -12 = 20X + 15
30X – 20X = 15 + 12 [On transposing 20X to L.H.S. and -12 to R.H.S.]
10X = 27
X = 27/10
Hence, X = 27/10 is the solution of the given linear equation.

Try these questions now:

1. 1/3x – 5/2 = 6 (Answer: x = 5/2)
2. x +7 -8x/3 = 17/6 – 5x/8 (Answer: x = 4)

Now try it yourself!  Should you still need any help, click here to schedule live online session with e Tutor!


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