This maths chapter deals with setting up an equation, solving an equation, and making equations from the solutions. You will learn the concept of transposing a number by solving more and more equations and moving numbers from one side to the other. The numbers can be transposed without adding or subtracting them from both sides of the equations.

Let us look at the most important topics of Chapter 4 Simple Equations:

• • • What is an equation? 

    • Parts of equation

    • Types of equations

    • Solving an equation

    • More equations

    • From solution to equation

    • Applications of simple equations to practical situations

The details of the different topics of Class 7 Maths Chapter 4 are as follows:

What is an equation?

In an equation, there is always an equality sign. The statement that supports the equality of two expressions and is connected by the equals sign "=" is called an equation in mathematics. The expression of the left-hand side (LHS) is always equal to the expression of the right-hand side (RHS). E.g.

2x – 4 = 9

Here,

2x – 4 and 9 are expressions

The equals sign “=” connects these two expressions.

 

Parts of an equation :

The equation mainly has six parts: coefficient, variable, operator, constant, term and last is expression. These parts are described with the help of an example. 

Equation is 2x – 4 = 9

Under this equation, 

Coefficient = 2

Variable = x

Operator = ➖

Constant = 4 and 9

Term = 2x, 4, 9

Expressions = both sides show expressions such as LHS = 2x – 4 and RHS with 9.

Types of equations:

There are mainly two types of equations in algebra: linear equations and polynomial equations. Other different types of equations are listed below:

• • Linear equations

  • Quadratic equations

  • Cubic equations

  • Differential equations 

  • Parametric equations 

Solving of equations:

Computation of the unknown variable by maintaining a balance of the equation on both the sides is known as solving an equation. It means that left hand side should be equal to the right hand side. The value we find out after balancing the equation is called the solution. Either LHS or RHS is interchanged, but it does not affect the equation, it remains the same. Solving an equation depends on the type of equation, such as it is linear, rational, parametric, etc. 

Steps in solving an equation:

The main aim to solve an equation is to find a solution that satisfies the conditions of the equation. The following steps are performed by balancing the equations on both sides. Steps are:

• • Addition property: On both sides, add a same number if x = y, then

         x + z = y + z 

• • Subtraction property: Also subtract a same number from both the sides if x = y, then x – z = y - z

  • Multiplication property: Multiply with a same number from both sides to find the value if x = y, then xz = yz 

  • Division property: In division property of equality, divide the same number into both sides. If x = y, then x/z = y/z (where z ≠ 0)

More equations:

Under this concept, you will learn about transposing of the equation. For transposing an equation, firstly, understand that transposing a number means moving it from one side to the other. We can transpose a number instead of adding or subtracting it from both sides of the equation. Transposing of the equation involves moving the terms to one side of the equation to find out the value of the variable. Simply stated, when terms move from one side to another, they change their sign.

Form solutions to equations:

The solutions to equations can be found by the normal path and reverse path. If we follow the normal path we get the solution, and if we follow the reverse path we will get the equation out of the solution. 

Equation ends with solution (normal path)

The solution ends with equation (reverse-path)

The equation is x = 5; if we multiply both sides with 3 will get the solution 5, and after that, if we divide it with 4 we get another equation from the solution. For example 

Start with                                         x = 5

 Multiply both sides by 4,               4x = 20                 Divide both sides by 4. 

Subtract 3 from both sides,            4x – 3 = 17           Add 3 to both sides.

 

Applications of Simple Equations To Practical Situations:

You must have seen various examples where statements in our routine language are taken and converted into simpler forms and equations. So far, we have learned how to solve simple and easy equations. Let’s move on to the next part and solve problems or puzzles from the practical solutions. The general method is to form the equations first and then solve them.