Page 45 - Maths Skills - 7

Simple Equations 43

INTRODUCTION
Rohan, Ridhima and Alisha constructed a game which they call Mind Reader. They want to present this game
to the whole class. The teacher appreciates their enthusiasm and invites them to present their game.
Alisha begins; she asks Amisha to think of a number, multiply it by 4 and add 5 to the product. Then, she asks
Amisha to tell the result. She says it is 65. Alisha instantly declares that the number Amisha had thought of is 15.
Amisha confirms.
The whole class including Amisha is surprised. It is Rohan’s turn now. He asks Balu to think of a number,
multiply it by 10 and subtract 20 from the product. He then asks Balu what his result is? Balu says it is 50.
Rohan immediately tells the number thought by Balu is 7, Balu confirms it.

Everybody wants to know how the ‘mind reader’ presented by Rohan, Ridhima and Alisha works. This chapter
will help us to know how the game works.

EQUATION

An equation is a condition of ‘variable’. The word ‘variable’ means something whose value can be changed. The
value of variable is not fixed. They are usually denoted by small letters like x, y, z, u, v, w etc. Expression can be
formed using various operations like addition, subtraction, multiplication and division on variables.

In an equation, there is always a sign of equality. This equality sign indicates that the value of the expression to
the right side of equality sign should be equal to the value of the expression to the left side of equality sign.

FORMING AN EQUATION
We can write a given statement in algebraic form. Here, we will learn to form an equation for a given statement.
For example, the sum of four times p and 7 is 20.
Here, four times of p = 4 × p Absorbing Facts
Sum = 4p + 7 Equation: Expression of variables which contain an equality
is means = sign ‘=’ is called an equation. i.e., x + y = 9 or x + y – 9 = 0
Result = 20 Polynomial: Expression of variables which does not contain
Thus, the required equation is 4p + 7 = 20 equality sign is called a polynomial. i.e., x + y – 4

Note:
(i) An equation must contain sign of equality. For example, 2x + 5 = 7 is an equation, but 2x + 5 > 7 or
2x + 5 < 7 are not equations, they are called inequations.

(ii) At least one of the two expressions (LHS or RHS) of an equation should have variable involved.
(iii) An equation remains the same when the expression on the left and right sides are interchanged.
(iv) An algebraic expression with sign of equality having one variable with highest power of variable as one
is called a linear equation in one variable. For example, 3x + 2 = 9 is a linear equation.

SOLUTION OF A LINEAR EQUATION IN ONE VARIABLE
The numerical value of the variable which satisfies the equation, i.e., makes both the sides equal is called the
solution of the equation. It is also called the root of the equation.
For example, let us check whether y = 2 is the solution or root of equation 2y – 4 = 0 or not.
2y – 4 = 0
putting y = 2 in LHS (Left Hand Side)
LHS = 2 × 2 – 4 = 4 – 4 = 0 RHS (Right Hand Side) = 0

Thus, LHS = RHS
Hence, y = 2 is the solution of the given equation.