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Example 7: Solve the following simple equations using transposition method.

7t
(a) 7p – 10 = 25 (b) 4(m + 3) = 16 (c) 4x − 1 = 6x – 5 (d) +1 =15
(e) 7x = 3x – 4 2
Solution: (a) 7p – 10 = 25

⇒ 7p = 25 + 10 (Transposing – 10 to RHS as +10)
⇒ 7p = 35
35
⇒ p = (Transposing × 7 to RHS as ÷ 7)
7
⇒ p = 5
(b) 4 (m + 3) = 16

16
⇒ (m + 3) = (Transposing × 4 to RHS as ÷ 4)
4
⇒ (m + 3) = 4
⇒ m = 4 – 3 (Transposing + 3 to RHS as – 3)

⇒ m = 1
(c) 4x − 1 = 6x – 5

⇒ 5 – 1 = 6x – 4x (Transposing + 4x to RHS as – 4x and –5 to LHS as +5)
⇒ 4 = 2x
Or 2x = 4

4
⇒ x = = 2 (Transposing × 2 to RHS as ÷ 2)
2
7t
(d) + 1 = 15
2

7t
⇒ = 15 – 1 (Transposing + 1 to RHS as – 1)
2
7t
⇒ = 14
2

⇒ 7t = 14 × 2 (Transposing ÷ 2 to RHS as × 2)
⇒ 7t = 28
28
⇒ t = (Transposing × 7 to RHS as ÷ 7)
7
⇒ t = 4
(e) 7x = 3x – 4 Remember

⇒ 7x – 3x = –4 (Transposing 3x to LHS as –3x) After simplification any side
of an equation (LHS or RHS)
⇒ 4x = –4
no quantity (number or
−4 variable) is left on any side,
⇒ x = = 1 (Transposing × 4 to RHS as ÷ 4)
4 it is taken to be zero (0).

137 Simple Equations