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Chapter 4 – Simple Equations

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

Introduction

Simple equations have an extensive application in our everyday lives. The application of simple equations to practical situations can be seen in the concept of balance. Let us have a closer look at what is an equation.

We know that an equation is a condition on a variable. Variable means something that changes or varies; it is never constant. It can be represented by an alphabet like x, or y or z or any other alphabet. These variables give us expressions like multiplication, addition, subtraction and division on the variables.

For an expression 2y +7, we multiply 2 with y and then subtract 7 from it. Here y is the variable.

Now, if we use the ‘=’ sign with the above expression, it becomes a simple equation.

Let us check the four steps of setting up an equation:-

1) Make each side of the equation simple.
For instance x – 7 = 10 – x
In the above, the left-hand side and right-hand side may not look similar. But when solved, they are the same as they balance the sides.

2) Take the variable on one side.
The following step in solving the equation is for any particular variable; you can use addition or subtraction to move the parts of the equation that include the variable, solving one side of the equals sign.

3) Isolation of the variable
In this step, the variable has to be isolated. For example,
7x+3=24
or 7x=24-3
or 7x=21
or x=21/7

4) Find the solution
Here, you must check if the solution is the one that is justified.
For example, in the above equation
x=21/7=3
so 7×3+3=24,
Let us see more equations,
2y+7=17

In the above equation, if we apply balance and shift the number 7 in the right-hand side of the ‘=’ sign, then it becomes 2y=17-7, i.e., + 7 becomes -7.
17-7=10, so now placing its value in the above equation, it becomes as follows:-
2y=17-7
i.e, 2y=10
so y=10/2

Therefore, the value of y is 5

    1. Find the value of y in 3y-2=7
    2. Find the value of x in 5y+2=17

They are:

1) Set up each side of the simple equation.

2) Taking the variable on one side.

3) Then, isolating the variable.

4) Finally, finding the solution.

This concept finds applications of simple equations to practical situations. Let’s learn more about it.

The left-hand side and the right-hand side of the equation is separated by a ‘=’ sign. In the equation, there are both variables as well as constants.

So, it is required to simplify the equation. On transposing or shifting the variables and constants from the left-hand side to the right-hand side, the plus sign associated with a particular constant or variable changes to a minus sign or vice versa. This is the concept of transposition.

Look at the following simple equation:

3x+2=5If we transpose 2 from the left-hand side to the right-hand side, it becomes:

3x=5-2

or 3x=3

or x=3/3=1

Simple equations are used to solve real-life problems. A simple equation deals with the relationship between two expressions that are on both sides of the equal sign. The clarity of the concept of simple equations will help you derive the solutions easily.

  1. How do you solve simple equations?
    While solving the simple equation, look at the equation as a balance, which has an equal sign ‘=’ at the centre. So, if you perform a change in one of the sides of the equation, you should remember to balance it with a change on the other side. This keeps the equation in balance.Example to find the value of x in the equationx + 3 = 5 You should get x on one side and subtract 3 from the other side.

  2. How do you introduce simple equations?
    It has the following components:-
    a) Variable: Denoted by alphabets, its values vary in the equation.
    b) Expression: It is formed by the functions of addition, subtraction, division and multiplication.
    c) Equation: It is an equality expression between two expressions.
    d) Solution to the equation: It gives the value of the variable with a variable on the left-hand side and a value on the right-hand side.
  3. What are the 4 steps to solving an equation or setting up an equation?
    As mentioned above, equations are nothing but a way of balancing the right-hand side of the equation with the left-hand side separated by an equal sign. Let’s check the steps:-
    1) Make each side of the equation simple.
    2) Take the variable on one side.
    3) Isolation of the variable
    4) Find the solution
    Therefore, the solution looks verified.
  4. What is the golden rule for solving equations?
    The golden rule of simple equations is to balance the equation so that the right-hand side and the left-hand side are equal. For this, all components of the equation, including the variables, are to be taken to the same side. There must be a separation of the variables applying multiplication or division or applying any other method. Find the solution and verify it as well.
  5. What are the types of equations?
    Different types of equations are

    • Quadratic equation
    • Exponential equation
    • Rational equation
    • Linear equation
    • Radical equation

For better conceptual learning of simple equations, please visit the mobile-based, high-quality video learning app with many videos of this subject for more clarity and understanding. These are designed for students between grades 6th to 12th. Download MSVgo Now!

High School Physics

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