Simple Equations in Algebra

Everything under the sun focuses on a particular type of balance. Even when the balance shifts to one side while you are cycling, you are likely to fall. It is mainly because the overall balance changes and causes collapse. 

However, it is the same with some mathematical equations as well. By now, you must have come across the ‘equal to’ sign (=) more than you can count. Like everything else, an equation has to be balanced as well. So, where can you put simple equations in this context? This article will help you to do just that.

What is a Simple Equation? 

In the simplest of terms, a variable and an ‘equal to’ sign make up a simple equation. Therefore, a simple equation is a mathematical representation of two expressions on either side of an ‘equal to’ sign. 

It mostly consists of a variable, frequently accompanied by a numerical constant. To understand this concept easily, consider the following example. 

3x – 4 = 5. It is a class 7 simple equation. In this representation, the x refers to a variable. Every equation of this category aims to find the value of x. However, you can also use other letters from the English alphabet to write a variable. 

Moreover, the value of 3x – 4 has to be equal to 5. Therefore, a simple equation of class 7 maintains the same value on either side of the ‘=’ sign. 

In this case, you can shift any number or variable from one side of the equation to the other. However, you have to keep in mind that the sign preceding the number changes as well. For example, a number with a negative integer transforms into a positive integer when it shifts to the other side. 

Coming back to this equation, you can take -4 to the other side in the following way – 

3x = 5+4 = 9.

Therefore, x = 9/3 = 3. Thus, the value of the variable x is 3. 

Solve the Sum 

1. In the simple equation 5x – 4 = 16, find the value of x. 

2. An equation stands as 10y + 25 = 125. Find the value of the variable y. 

Now you know what a simple equation means. However, before solving simple equations, you will have to understand what transposition stands for.  

1. What is Transposition in a Simple Equation? 

In its most primary sense, transposition implies when you shift a variable or a number to the other side of ‘=’. It is one of the most vital functions of simple equation sums. 

To be able to understand this further, you will have to keep in mind the signs preceding a variable or a number. As you shift a number to the other section; its sign changes. For instance, ‘+’ becomes ‘-‘ and ‘-‘ turns into ‘+’ when it changes sides. 

Consider the following example – 

50x – 20 = 980.

Therefore, 50x = 980+20

50x = 1000

x = 1000/50

Or, x = 20. 

As you can see in this particular simple equation in mathematics, -20 becomes +20 on the other side. It refers to an easy example of transposition. 

In the next section, you will learn about the real-life applications of simple equations. 

What is the Difference Between Variables and Constants in a Simple Equation?

Without a variable, a simple equation does not exist. So, what is a variable? A variable is that unknown factor of a simple equation whose value needs to be derived through solving the equation. A variable is often denoted by generic alphabets such as x, y, z. The quantity of this variable will change if the equation changes even by a fraction of a number. However, when the simple equation aims to find a particular quantity like time, distance or speed it is suggested to use a variable that represents these specified quantities- t for time, d for distance and s for speed.

A constant is a fixed number or the number that is provided in the simple equation whose value is known. A constant never changes its value and it is through the transposition of the constants that the simple equation is solved further to find out the unknown value of the variable.

For example, in 4 – x = 1, 4 and 1 are the known constants while x is the unknown variable.

What are the Other Methods of Solving Equations?

We have seen above that a simple equation can be solved by the transposition method, in which the constants are taken to the other side of the equation (LHS or RHS) to find the value of the variable. However, this is not the only method through which a simple equation can be solved. There are two additional methods that a student can use to find the value of the variable.

Before understanding the other two methods, let us know what the terms LHS and RHS stand for. The LHS stands for the Left-Hand Side and RHS stands for the Right-Hand Side of the two expressions that are equated by the equal to ‘=’ sign.

Now let us look at the other two methods of solving a simple equation: 

1. The Trial-and-Error Method

As the name suggests, trial and error are a method that involves trying out different solutions for the equation. Different values of the variable are guessed, normally starting from the smallest number 1, and whichever solution brings LHS=RHS is the correct value.

For example, let us take x + 5 = 9.

In the above equation, LHS is x + 5 and RHS is 9. To solve the equation LHS should be equal to RHS.

So, our next step will be to try out different values of x and whichever value will give the result as 9 will be the correct value.

Hence, LHS=RHS at x=4.

2. The Systematic Method

If you think about it, an equation is like a weighing scale in which LHS needs to be exactly equal to RHS in order to have a proper balance of the scale. Only after adding, subtracting, multiplying or dividing the exact quantity into both sides of the weighing scale will it be perfectly balanced i.e., make the equations equal.

The systematic method works in the same manner of adding or removing the exact numbers from both LHS and RHS to derive the value of the variable.

Following are some examples of simple equations:

• Equation where we Add

x – 77 = 3

on adding 77 on both the sides we get

x – 77 + 77 = 3 + 77

So, x = 80

• Equation where we Subtract

y + 36 = 50

on subtracting 36 on both the sides we get

y + 36 -36 = 50 – 36

So, y = 14

• Equation where we Divide

9x = 27

on dividing 9 on both the sides we get

9x/9 = 27/9

So, x = 3

• Equation where we Multiply

y/2 = 10

on multiplying 2 on both the sides we get

y/2 x 2 = 10x2

So, y = 20

• Equations where there are Multiple Steps

2x + 3 = 11

on subtracting 3 from both the sides we get

2x + 3 – 3 = 11 -3

2x = 8 

then dividing 2 on both sides we get

2x/2 = 8/2

 So, x = 4

What is the Application of Simple Equations? 

Suppose you have Rs.1000, out of which you can spend Rs.300 on video games. With the remaining money, you will have to purchase some books from a particular series. After reaching the market, you see that each book costs Rs.70. 

So, how many books should you buy so that you still have Rs.300 left for video games? It is where simple equations class 7 standard will come to your rescue. 

Assume that x stands for the number of books you can buy at Rs.70 per book. Therefore, the equation becomes – 

70x + 300 = 1000

70x = 1000-300

70x = 700

x = 700/70

Therefore, x = 10. Thus, you can buy 10 books @Rs.70 and still be able to keep Rs.300 for your video games. However, you should also know about solving simple equations with fractions. 

How to Solve a Simple Equation with Fractions? 

Take into account the following example of a simple equation with fractions – 

½  x + ⅘ = 1 ⅙ 

So, how will you find the value of x in this equation? Transpose ⅘ to the other side and convert the mixed fraction into an improper fraction. 

Therefore, \[\frac{1}{2}x=\frac{7}{6}-\frac{4}{5}\]

 \[\frac{1}{2}x=\frac({(7 \times 5)}-{(4 \times 6)}){30}\]

 \[\frac{1}{2}x=\frac{((7 \times 5)-(4 \times 6))}{30}\] , since the LCM of 5 and 6 is 30. 

\[\frac{1}{2}x=\frac{(35-24)}{30}\] 

 \[\frac{1}{2}x=\frac{9}{30}=\frac{3}{30}\] 

\[x=\frac{3}{10}\times2\] 

Therefore, the value of x is 3/5. 

Now that you know about this concept, it is time to take a look at simple equation exercises. 

Simple Equations for Class 7 NCERT

Solve the following NCERT maths class 7 simple equations to improve and sharpen your understanding – 

• Write the following statements in the form of simple equations: 

1. The sum of five times y and 15 is 32. 

2. One-third of a number plus 5 is 8. 

3. The sum of two consecutive odd numbers is 54. Form a simple equation and find the value of the numbers.

• Consider the following equation:

1. Shyam’s father’s age is 5 years more than three times Shyam’s age. Shyam’s father is 44 years old. Set up an equation for this situation and find Shyam’s age. 

2. The breadth of a rectangle is four times its length. If its perimeter is 90 cm, find the length and breadth of the rectangle respectively.

3. A boy travelled one-third of his journey by foot and one-fifth by a car and the remaining 2 km by a rickshaw. What is the total distance he covered in kilometres? 

This article, therefore, sheds light on the definition, example, and nature of simple equations. However, you can look out for other similar interesting topics on the website of Vedantu. You can also download our Vedantu app for enhanced access.