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Forming Simple Equation From a Solution

Let us take a variable x = 3. Consider it a solution of an equation. Can you make the equation using
x = 3?

Pihu always thinks differently. She looks at successive steps that one takes to solve an equation.
She wonders why not follow the reverse path:
Equation Solution (normal path) If we follow the reverse path with
Solution Equation (reverse path) each step in the equation 4x - 3
=17, we get the solution of the
She follows the path given below: equations. As, add 3 to both sides,
She starts with x = 5 we get 4x = 20. divide both sides
Multiply both sides by 4, and gets 4x = 20 by 4, we get x = 5.
Now, she subtracts 3 from both sides, and gets 4x – 3 = 17

This has resulted in an equation. create and solve
Thus, we can make an equation with solution x = 5. For x = 3, make three different

Now, Aarav starts with the same first step x = 5 and builds up equations. Ask your friend to
another equation. solve these equations. Check

Multiply both sides by 3, and he gets, 3x = 15 whether they get the same
solution or not.
Then, he adds 4 to both sides, and he gets, 3x + 4 = 19
Here, we can see that different equations can be formed for the same solution.
Thus, for a given equation, we get only one solution; but for a given solution, we can make many
equations.

Practice Time 6C

1. Solve the following equations by using the transposition method.
(a) 3x + 2 = 11 (b) 9 – 7y = 54 (c) 3(y – 2) = –18 (d) 3 (p – 1) + 6 = 12
2p x − 2
(e) −= 14 (f) =1 (g) 4 + 5(t – 1) = 34 (h) 0.6x – 2.4 = 0.3
4
3 3
2t − 4 a
(i) 4(x – 7) – 3 = 9 (j) += 9 (k) −= − 4 (l) 0 = 16 + 4 (x – 6)
3
3
5 2
2. Form four equations starts with the solution:
(a) x = –2 (b) x = 4

Application of Simple Equation to Practical Situations

Here, we shall study the formulation and solution of some practical problems. The procedure to
translate a word problem in the form of an equation is known as the formulation of the problem.
It consists of two parts: formulation and solution.
These problems include unknown quantities and known quantities stated in words.

A word problem is first translated in the form of an equation containing unknown quantities and
known quantities and then solved to get the value of unknown quantities.

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