## Raj Sharma

I would like to share learning-related tips and tricks for lifelong learners

Algebra is a mathematical branch that deals with numbers and symbols along with the techniques to solve them. These symbols or letters are nothing but the missing numbers, technically called ‘variables’, in the mathematics terminology.

These are called variables as their value is not fixed and changes with the change in the nature of operation or expression. Therefore, the algebraic expression can also be said to define the relationship between variables, just as sentences describe the relationship between the words.

Calculating the basic maths expression with basic addition and subtraction expression is easy. However, solving these mixed equations is not easy. Doing Algebra problems is a difficult task for the students, as they get puzzled by the added letters between the numbers in the equation and struggle through the problems for hours. To make it easy for them to do algebra, here are few tips on “How to do Algebra”. These will help students arrive at the solution in the quickest manner.

## How to do Algebra

#### Begin with defining the Operation order –

To solve the algebra sum, firstly it is essential to know the order of operation. The order stands as - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. To remember this order, it is good to remember the Acronym “ PEMDAS.” So, when trying to solve algebra expression, always follow this order, i.e., begin with the Parentheses, if there is one in the question.

Then, look for exponents and solve them. Similarly, after solving Parentheses and Exponents, perform the multiplication, division, addition, and subtraction, in the mentioned order.

While solving the Parentheses, students shall follow the same order of operation as PEMDAS. Also, students can perform ‘division’ and ‘multiplication’ simultaneously, as, ‘Addition’ and ‘Subtraction.’ For instance, (3+10)*5 - 8/6

This equation will be solved as

(3+10) = 13

13*5=65

65 – 8/6

65-1.33 = 63.67

#### Deal with the negative numbers in the equation –

A negative number is a number represented on the opposite side of the positive number on the number line. There are specific rules regarding negative numbers such as,

The two negative numbers add up to become a lower number.

Two negative signs in the equation cancel outs to become positive, that is, multiplying or dividing two negatives gives positive.

However, multiplying and dividing one negative and one positive gives negative only.

#### Organizing the equation –

Algebra equations are generally associated with long operations. The equation can become tough and confusing if, too many operations are performed in the one-step, such as,

in the equation “ 9/3 - 5 + 3 × 4”,

do not solve 9/3 and 3*4 in the same step.

Rather, either multiply in the first step and divide in the second or, divide in the first step and multiply in the second.

This way, the equation remains organized and does not lose its operations.

#### Variables as “unknown valuables” –

In algebra questions, there is a mix of numbers, signs, and alphabets. Each of them has a meaning in the equation. The symbol such as, ‘π’ termed as ‘pie,’ has a value of ‘3.14159’. Similarly, the alphabets such as, ‘x,’ ‘y,’ ‘z’ representing the variables are basically numbers without any assigned values. The equations with such variables, have to be solved for arriving at their value. For Instance, it is given that, solve – 2x+5=10

Here, x is the variable and equation has to be solved for it, as below

2x+5=10

Step 1 – organize the equation by combining the constant terms on one side, such as 2x=10-

Step 2 – perform the Subtraction operation, such as 2x=5

Step 3 – solve for the value of X, such as X=5/2=2.5

Also, there can be a recurring variable, that is, the variable can appear more than once, in the equation. For example, 6x+10x-2x = 55

In such cases, the trick to solve is to simplify the same variable simultaneously. Therefore, the above example can be solved as

6x+10x-2x = 55

Step 1 – combine the variables on one side and perform the operation of addition, such as 16x-2x=55

Step 2 – Now, perform the operation of subtraction as, given by, the rule of PEDMAS, such as 14x=55

Step 3 - solve for X, X=55/14 = 3.92

However, in such cases of recurring variables- the variable with the same exponents can, only, be combined together. For instance,4x2+2x+3x=5. Here, out of the three variable terms, two have the same exponents. Hence, only these two variable terms can be combined as, 4x2+5x=5

Therefore, the students shall be conscious while simplifying the variables in the equation. The same variable with the same exponential value can be solved together. Apart from the linear equation, algebra can also be performed on the quadratic equation with the same set of rules.

#### Solving for operations on both the sides of the equation –

If the equation has the operation on both sides, the solving strategy will be, taking the variables on one side, while keeping the known values on another side. Always remember when a value or variable is moved from one side to another its sign gets change.

For example, there is an equation 2x+3=4x+5, then, begin with combining variable terms and numerical terms at opposite sides, such that the equation will look like 2x-4x=5-3. Observe here, previously the equation had positive ‘4x’ and ‘3’ but as the side gets reversed, the signs changes to negative.

Now, to get the answer, solve it by the rule of PEDMAS and basic maths. Therefore, step two will be operating‘ addition’ on both sides. This will give, -2x=2. This shall now be solved for x, that will be, x= -2/2=1. Here, the value of x achieved is the negative one.

#### Solve through ‘canceling’ –

The other approach to solve the algebra equation is to solve through canceling. An example can best explain this approach. Let’s say; there is the equation: x+5=10*4

Then this can be solved as,

Step 1 – To eliminate the numerical value, subtract that value from both the side, such as x+5-5=10*4-5

Step 2 - The subtraction will lead to elimination of value from one side, leaving only with the variable on one side, while the rest of the equation with the numerical on the other hand, such as x = 40-5

Step 3 - Solving gives, x = 35

Similarly, multiplication and division can be canceled, from the equation to arrive at the solution. For doing so, the student has to develop the equal and opposite relationship, as the rules say for multiplication and division. Such as, for solving through canceling for the equation, 6x = 14+2, the steps will be

Step 1 – Eliminating the numerical ‘6’ that is in multiplication with the variable. For this divide both the sides with ‘6’ ,such that, X = (14 + 2)/6

Step 2 – performing the operation to arrive the value of X, therefore, X= 16/6= 2.66

In a similar way, if the equation has exponents, it can also be canceled. As known, by the rules of pre-algebra and basic mathematics, the opposite of exponent is root. Therefore, for canceling the exponent, the root has to be taken. For instance, x2 = 81, x = √81 = 9

#### Solve though factoring –

Once, basic algebra has been learned, the students can move towards the advanced strategy that utilizes factoring techniques. It becomes very easy to solve the equation by factoring as it decomposes the complexity of the equation into simplicity.

For instance, if the equation is in the form of

“ ax + ba” - factor it to “a(x + b)”, example : 4x + 4 = 4(x + 1)

“ax2 + bx”- factor it to “cx((a/c)x + (b/c))”, example: 12y2 + 24y = 12y(y + 2)

“x2 + bx + c” - factor it to “(x + y)(x + z)”, example: x2 + 4x + 3 = (x + 3)(x + 1).

#### Solve through the graph –

Graphs are another tool to arrive at the solution for algebraic expression. The equation with two variables can be easily solved through a pictorial description. The graph is said to have two-axis- x-axis and y-axis. The values associated with each variable in the equation is being plotted on these axes to arrive at the solution.

Simply, plug-in, the value for either ‘x’ or ‘y’ and solve for the other. Then, plot these values on the graph on the gives points. For example, there is an expression 2x=y, than, putting x =1 will give y=2. Plot (1,2) coordinates on the respective axis to arrive at the solution.

#### Solve word problem with logic –

The strategy to solve the algebra-based word problems is to convert them into the equation form and plug in the basic value and check for their validity. For instance, after forming the equation, check whether the equation holds true for different values of x.

#### Do not strive to get an integer as an answer for algebra, always –

After solving the algebra question; it is not always necessary that you get an integer. The answer can be in the form of a decimal, fraction, or with the exponent. For example, if for the algebraic expression, the solution has been arrived as, x=73. By using the calculator, we can find the value of 73, like 1.91. However, it is advisable to write 73 as 73 only, rather than calculating it and writing it in decimal.

#### Equations with Inequality –

It is not necessary that every equation will have an equality sign. There can be such equations as well, where there is the sign of inequalities, such as ‘>’ ( that is, greater than) or ‘<’ ( that is, less than). This kind of equation is solved with the same set of rules. Follow the PEDMAS, organize the equation by keeping the variables on one side and constant on other, solve each operation one-by-one, don’t hassle between the two operations, and arrive at the solution. The only difference here will be instead of the sign of “=” (equality), there will sign of ‘>’ ( representing, greater than) or ‘<’ ( representing, less than).

For instance, solve 4>2x+5

Step 1 – organize the equation by bringing constant terms on one side. The equation will become – 4-5>2x

Step 2 – solve for operation “subtraction” and get, -1>2x

Step 3 – Solve for X, to get, -1/2>x or -0.5>x

Here, the solution will be the variable ‘x’ is less than -0.5. That is, X, can be -1,-2, and so on.

#### Solving two equations simultaneously –

Generally, the two equations are solved through graphs, by plotting their coordinates, the solution for the equation is being arrived at. However, if the equations are with basic operations, it is advisable to solve them simultaneously by performing the given operations. Such as,

Suppose it is given that,

X= 3y-4 and x= -y-5

The solution will be worked out as –

Step 1 – plug in the value of X from one equation to the other. Such as,

3y-4 = -y-5

Step 2 – organize the equation by collecting the variable terms and constant terms on opposite sides, such as

3y+y = -5+4

Step 3 – perform the addition operation on both the side, such as

4y =-1

Step 4 – solve for y, such as

Y=-1/4=-0.25

The above are just a few of the tricks and strategies that can be adopted while dealing with algebraic expressions. If these basic rules are followed and performed, surely the equation can be solved without any hassle in the quickest time and least steps.

However, to attain expertise in arriving at the solution, practicing the equation solution is essential. The more you solve, the more you will learn. Try solving different expressions with different combinations of operations. This will help in learning and building up the Math concept better.

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Become trustworthy
To level up your mental game

Empower your mind to conquer any obstacle that comes your way! You have the strength within you to overcome any challenge.

Here are 5 exciting opportunities to level up your mental game. Let's dive in and discover the potential within you!

Forgiveness is important in our life
Ways to develop empathy
20 points of Rich mindset

1. Rich mindset people know exactly why they are doing what they are doing!

2. Rich mindset people do not do things that are not aligned to their Why.

3. Rich mindset people know what they are passionate about!

4. Rich mindset people work only on what they are passionate about!

5. Rich mindset people's life is filled with excitement and more happiness!

6. Rich mindset peoples are the master of their craft because they are passionate about it!

7. Rich mindset people have big juicy goals.

8. Rich mindset people write down goals every single day.

9. Rich mindset people are most vocal about their goals.

10. Rich mindset people will never reduce goals but increase the effort.

11. Rich mindset people think that money is everywhere!

12. Rich mindset people are plenty of opportunities provided they try to grow their knowledge and skills.

13. You become rich twice, first in your mind and then in reality.

14. Rich mindset, people are the creators.

15. Rich mindset people know that It is effortless to make Money.

16. Rich mindset people know money is available in abundance.

17. Rich mindset people create multiple sources of income.

18. Rich mindset peoples are very health-conscious people.

19. People admire a Rich mindset, people's discipline, and good health.

20. Rich mindset people spend lots of quality time with family.

19 points of Broke mindset

1. Broke mindset people think everything is too good to be true.

2. Broke mindset people give up when things don't go their way; a few disappointments, and they are onto something else, saying things like "it wasn't for me."

3. Broke mindset people always have an excuse.

4. Broke mindset people think that not getting what they want is OK.

5. Broke mindset always has to talk it over with their broke friends to make sure no one will make fun of them if they make a decision.

6. Broke mindset people are never coachable and teachable.

7. Broke mindset people are scared of others.

9. Broke mindset people are glad when the day is over.

10. Broke mindset people think rich people are lucky.

11. Broke mindset people work by the hour.

12. Broke mindset people want to know that after 1 hour of work, they have something to show.

13. Broke mindset people get excited; they just got hired.

14. Broke mindset people complain a lot.

15. Broke mindset people are too concerned about what other people are doing.

16. Broke mindset, people think that if no one is doing something, it must suck.

17. Broke mindset people think that if everyone (all 200 people at a meeting or on a conference call) are all doing the same thing, it must be saturated.

18. Broke mindset people think it is OK for other people to live where they want to live, drive what they want to operate and do what they want to do.

19. Broke mindset people are OK with the fact that they can't do these things.

The 20 Days personal growth challenge

1. Listen more before you speak. Try to understand what you are trying to say before then reply.

2. Try before quitting. At least try things whatever you want in your life. Never quit before trying.

3. Whenever you are going to write something anywhere, think before you write.

4. Spend money, but first, earn. Earn before you spend.

5. Believe first before doing anything in your life. Believes are valuable in every situation.

6. Live your life; enjoy each moment in your life. Live before you die.

7. Whenever you go to start anything, prepare first. Prepare before you start.

8. Make time for health. Exercise and meditate before you get stressed.

9. To be happy and for piece live in present moments. With the plan of the future, never invest in your present. Live it.

10. Understand the rules of freedom before you expand your freedom.

11. Love yourself and spread that love before time goes away.

12. Accept and solve the situation before you miss out.

13. Be responsible before time has gone. Be responsible when you need it. If time goes, it never comes again.

14. Take permission from your family before taking any kind of action.

Student success plan

Being a successful student is not a child's play. It requires utmost devotion, a student success plan, hard work, and a passion for being successful in life. If you genuinely wish to be a successful student in High school or college, there are student success strategies that can prove to be helpful to the achievement of your goal.

1. Prioritization

2. Punctuality

3. No cheating

4. Concentrate

5. Refraining from unnecessary comparisons

6. Improvement in progression

7. Curiosity and excitement

The importance of self study

One of the best ways to absorb a piece of information in your mind is to read about it on your own with full focus.

When you have a solid game plan before starting any study session, it naturally improves your productivity. This way you can be ensured that you make each session as productive as possible and make the best out of your time.

It means that you make a timetable in order to enjoy a productive day along with getting yourself nearer to success every day. Along with social activities make sure that you prescribe a fixed number of hours to study each day.

6 student success strategies

1.) Pay attention

Paying attention in class is one of the most crucial practices a successful student is required to do.

2.) Taking notes

It is not possible to remember every word the teacher says. So, it is essential that you jot down notes in the form of main points that summarize what the teacher is explaining.

3.) Clarifying doubts

To avoid being lost during a lecture make sure that you clarify all your doubts.

4.) Avoiding distractions

5.) A positive relationship with your teacher

Determines the success of an individual in high school and college is his/her relationship with the teachers and staff.

6.) Have fun

Along with studying it is essential for every student to have a carefree time where he/she can just have some fun and relax with friends.

How to write an essay fast and well

Write a compelling and catchy introduction. Mention an interesting fact related to your topic into the intro.

How to write the middle part of the essay?

The primary focus is on the 1st body, this paragraph need not be as catchy as the previous stages. So, here you can mention some weak points in order to elaborate on the essay further.

The first paragraph - Write the strongest points or essential facts in the first paragraph

The second paragraph - Tries to elaborate of an essay further and adds more intriguing points.

The third paragraph - Cite some exciting examples with catchy tone related to the topic in the third paragraph

How to end an essay

Who do not understand how to conclude an essay without sounding abrupt. Even though the conclusion is supposed to be short and sweet, it is an underrated part of an essay, and most of the students seem to be ignorant of how they should end an essay.

The majority of the students fail to understand is the fact that a proper link between the introduction and the conclusion of an essay can prove to be extremely fruitful.

If you have stated an idea in the intro, you can add a line or two elaborating that point in the conclusion. Expand the theme that you introduced in the intro without making it seem like you are merely repeating a certain fact to fill up pages.

4 Major types of essays

Since essays have become an integral part of the various school and college assignments along with applications to prestigious universities, students cannot afford to stay ignorant about the types.

Before diving straightaway into looking for all sorts of essay help online, here are four major types of essays every student should know about. It is easy to get confused with the immense number of topics in essay books.

However, the types of essays are limited, and they are more manageable than you can actually think of! These four types mainly cover all the other subtypes, so, let us take a look.

1.) Narrative essays

2.) Descriptive essays

3.) Expository essays

4.) Persuasive essays

Smart studying with online tools

THERE ARE SEVERAL ONLINE RESOURCES AND TOOLS TO HELP YOU ASSIMILATE A LARGE AMOUNT OF STUDY MATERIAL QUICKLY AND EFFECTIVELY.

Right mindset

To create the right mindest that will ensure your success. This entails accepting change and aiming to grow and improve constantily.

Importance of a positive attitude in life

A positive attitude brings out creativity in thinking and you will get new ideas for improving the subjects. Positivity will also help in finding better solutions to the problems. Even in a school or college project or assignment, a positive attitude will bring out better results. It will also help in keeping your mind relaxed and calm in negative situations.

Having a positive attitude will attract more people to you. You can be the leader of your group and lead people to follow a positive attitude in life. You can remove the negativities in yourself and others too. It will improve your life to a large extent. With a more positive attitude, you will get more able to solve any problem in life.

Optimism always leads to success. Positivity will give more enthusiasm to work which will result in promotions and increments. This is the reason why people with a positive attitude become successful in later life.

A positive attitude will gain more friends. It is because negativity will reduce your self-confidence and you will get discouraged. People will like staying with positive people. Positivity will spread happiness and joy all around the place.

10 steps to effective listening

Here are the ten steps that can help you to have effective listening:

1.) Face the speaker and always maintain eye contact.

2.) Pay attention, but be relaxed.

3.) Have an open mind and listen to them without judging them.

4.) Carefully listen to the words and try to understand what the speaker is saying.

5.) Never interrupt the speaker, nor impose your thinking on them.

6.) When the speaker takes a pause only then ask a question.

7.) Never ask things unnecessarily, only ask to have a better understanding.

8.) Try to feel what the speaker is feeling and communicating.

9.) Try to give simple and regular feedback to the speaker.

10.) Focus on non-verbal cues like facial expressions and gestures.

Smart study

Choose your subjects of interest, understand that not all the assignments and classes will be equally interesting.

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#### My Group

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Informative visual post. I love ot

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Wow awesome Infographic

• ###### How to study online for the best results

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