NCERT Class 6 Mathematics Text book for Blind Students made Screen Readable by Professor T K Bansal.

Let us recall the matchstick pattern of the letter L given in Fig 11.1. For our convenience, we have the Fig 11.1aa redrawn here.

Figure 11.1aa

The number of matchsticks required for different number of L’s formed was given in Table 1. We repeat the table here.

Table 1

We know that the number of matchsticks required is given by the rule 2n, if n is taken to be the number of L’s formed.

Arjun always thinks differently. He asks, “We know how to find the number of matchsticks required for a given number of L’s. What about the other way round? How does one find the number of L’s formed, given the number of matchsticks”?

We ask ourselves a definite question.

How many L’s are formed if the number of matchsticks given is 10?

This means we have to find the number of L’s (i.e. the value of n), given the number of matchsticks 10. So,

2n = 10 .. .. .. (1)

Here, we have a condition to be satisfied by the variable n. This condition is an example of an equation.

Our question can be answered by looking at Table 1. Look at various values of n. If n = 1, the number of matchsticks is 2. Clearly, the condition is not satisfied, because 2 is not 10. We go on checking.

Table

We find that only if n = 5, the condition, i.e. the equation 2n = 10 is satisfied. For any value of n other than 5, the equation is not satisfied.

Let us look at another equation.

Bhaarat is 3 years younger than Rajeev. Taking Rajeev's age to be x years, Bhaarat’s age is (x − 3) years. Suppose, Bhaarat is 11 years old. Then, let us see how our method gives Rajeev’s age.

We have Bhaarat’s age, x − 3 = 11 .. .. .. (2)

This is an equation in the variable x. We shall prepare a table of values of (x − 3) for various values of x.

Table

Complete the entries which are left blank. From the table, we find that only for x = 14, the condition x − 3 = 11 is satisfied. For other values, for example for x = 16 or for x = 12, the condition is not satisfied.

Rajeev’s age, therefore, is 14 years.

To summarise, any equation like the above, is a condition on a variable. It is satisfied only for a definite value of the variable. For example, the equation 2n = 10 is satisfied only by the value 5 of the variable n. Similarly, the equation x − 3 = 11 is satisfied only by the value 14 of the variable x.

Note that an equation has an equal sign (=) between its two sides. The equation says that the value of the left hand side (LHS) is equal to the value of the right hand side (RHS). If the LHS is not equal to the RHS, we do not get an equation.

For example : The statement 2n is greater than 10, i.e. 2n > 10 is not an equation. Similarly, the statement 2n is smaller than 10 i.e. 2n < 10 is not an equation. Also, the statements (x − 3) > 11 or (x − 3) < 11 are not equations.

Now, let us consider the equation; 8 − 3 = 5

There is an equal sign between the LHS and RHS. Neither of the two sides contain a variable. Both contain numbers. We may call this a numerical equation. Usually, the word equation is used only for equations with one or more variables.

Let us now, do an exercise.

State which of the following are equations with a variable. In the case of equations with a variable, identify the variable.

Following are some examples of an equation. (The variable in the equation is also identified).

Fill in the blanks as required :