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Practice Time 6B

1. Solve the following simple equations using balancing (systematic) method. Also, Verify your result.

y
(a) x + 7 = 12 (b) x – 8 = 3 (c) 4x = 32 (d) = 6
4
(e) 3x – 7 = 5 (f) 7 + z = 19 (g) 2t + 3 = 13 (h) y – 3 = 9
7
7
10p + 4 3
(i) 12 – 5y = 2 (j) 8 + 6y = 20 (k) =− 9 (l) 4y − = 1
3n 3 3u − 1 4 5
(m) = (n) = 2
7 2 4

Transposition Method

Grandfather to Pihu: Pihu! there is another method to solve a simple equation as I told you earlier.
It is called transposition method. Transposition is nothing but balancing the other side of equality
when we make any change on one side.

In transposing, transferring the quantity is same as adding or Transposing means changing
subtracting the number from both sides. In doing so, the sign of the the side of a quantity or
number has to be changed. transferring a quantity from
one side to other side.
Let us take the equation, i.e., 2x + 3 = 73 … (i)

2x + 3 – 3 = 73 – 3 (Subtracting 3 from both sides)

⇒ 2x = 70
Or 2x = 73 – 3 … (ii)

You can observe from equation (i) and (ii) that from LHS 3 is transferred to RHS with opposite
sign (–).

Now, 2x = 70 …(iii)
2x 70
= (Dividing both sides by 2)
2 2

x = 35
1
Or x = 70 × = 35 …(iv)
2
Similarly, from (iii) and (iv), we can also observe on dividing by 2 to both sides of the equation,
we get the solution.

Thus, we can say, when we move (transpose) a term from one side to the other, the mathematical
operations inverses to make the equation balanced.
In transposition:
Hence, while transferring a number or a quantity from one side to the + –
another side (LHS to RHS or RHS to LHS), the sign of the quantity is changed – +
÷
×
as + to –, – to +, × to ÷, and ÷ to ×. ÷ ×

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