NCERT Book Class 7 Maths Simple Equations

Simple Equations

4.1 A MIND-READING GAME!

The teacher has said that she would be starting a new chapter in mathematics and it is going to be simple equations. Appu, Sarita and Ameena have revised what they learnt in algebra chapter in Class VI. Have you? Appu, Sarita and Ameena are excited because they have constructed a game which they call mind reader and they want to present it to the whole class.

The teacher appreciates their enthusiasm and invites them to present their game. Ameena begins; she asks Sara to think of a number, multiply it by 4 and add 5 to the product. Then, she asks Sara to tell the result. She says it is 65. Ameena instantly declares that the number Sara had thought of is 15. Sara nods. The whole class including Sara is surprised. It is Appu’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. Appu immediately tells the number thought by Balu. It is 7, Balu confirms it.

Everybody wants to know how the ‘mind reader’ presented by Appu, Sarita and Ameena works. Can you see how it works? After studying this chapter and chapter 12, you will very well know how the game works.

4.2 SETTING UP OF AN EQUATION

Let us take Ameena’s example. Ameena asks Sara to think of a number. Ameena does not know the number. For her, it could be anything 1, 2, 3, . . ., 11, . . . , 100, . . . . Let us denote this unknown number by a letter, say x. You may use y or t or some other letter in place of x. It does not matter which letter we use to denote the unknown number Sara has thought of. When Sara multiplies the number by 4, she gets 4x. She then adds 5 to the product, which gives 4x + 5. The value of (4x + 5) depends on the value of x. Thus if x = 1, 4x + 5 = 4 ×1 + 5 = 9. This means that if Sara had 1 in her mind, her result would have been 9. Similarly, if she thought of 5, then for x = 5, 4x + 5 = 4 × 5 + 5 = 25; Thus if Sara had chosen 5, the result would have been 25.

To find the number thought by Sara let us work backward from her answer 65. We have to find x such that 4x + 5 = 65 (4.1)

Solution to the equation will give us the number which Sara held in her mind. Let us similarly look at Appu’s example. Let us call the number Balu chose as y. Appu asks Balu to multiply the number by 10 and subtract 20 from the product. That is, from y, Balu first gets 10y and from there (10y – 20). The result is known to be 50.

Therefore, 10y – 20 = 50 (4.2) 

The solution of this equation will give us the number Balu had thought of.

4.3 REVIEW OF WHAT WE KNOW

Note, (4.1) and (4.2) are equations. Let us recall what we learnt about equations in Class VI. An equation is a condition on a variable. In equation (4.1), the variable is x; in equation (4.2), the variable is y.

The word variable means something that can vary, i.e. change. A variable takes on different numerical values; its value is not fixed. Variables are denoted usually byletters of the alphabet, such as x, y, z, l, m, n, p etc. From variables, we form expressions. The expressions are formed by performing operations like addition, subtraction, multiplication and division on the variables. From x, we formed the expression (4x + 5). For this, first we multiplied x by 4 and then added 5 to the product. Similarly, from y, we formed the expression (10y – 20). For this, we multiplied y by 10 and then subtracted 20 from the product. All these are examples of expressions.

The value of an expression thus formed depends upon the chosen value of the variable. As we have already seen, when x = 1, 4x + 5 = 9; when x = 5, 4x + 5 = 25. Similarly, when x = 15, 4 x + 5 = 4×15 + 5 = 65; when x = 0, 4 x + 5 = 4 × 0 + 5 = 5; and so on.

Equation (4.1) is a condition on the variable x. It states that the value of the expression (4x + 5) is 65. The condition is satisfied when x = 15. It is the solution to the equation 4x + 5 = 65. When x = 5, 4x + 5 = 25 and not 65. Thus x = 5 is not a solution to the equation. Similarly, x = 0 is not a solution to the equation. No other value of x other than 15 satisfies the condition 4x + 5 = 65.

Please refer to attached file for NCERT Class 7 Maths Simple Equations