Page 170 - Maths Class 06

(f) A number exceeds 5 by 3.

(g) If 12 is subtracted from a number, the result is 24.
(h) Twice a number subtracted from 19 is 11.
(i) 6 times a number is 5 more than the number.
(j) A number divided by 8 gives 7.

2. Write a statement for each of the equations, given below:
(a) 3 - x = 7 (b) x + 7 = 10 (c) x - 7 = 5
x
(d) 2x + 4 10= (e) 11+ x = 17 (f) = 7
5
3. Verify by substitution that:
(a) the root of 3 +2x = 9 is x = 3 (b) the root of 3x – 5 = 7 is x = 4

(c) the root of 8 – 7y = 1 is y =1 (d) the root of 5x – 8 = 2x – 2 is x = 2
z
(e) the root = 8 is z = 56
7
4. Solve each of the follow ing equations by the trial-and-error method:
x
(a) = 3 (b) 3x = 9 (c) 2x + 4 = 3x
2
(d) x + 7 = 7 (e) x - =3 7 (f) x + 5 = 8

(g) 2x + 3 = 3x (h) 10 - x = 6 (i) x - 4 = 2 x - 6

Systematic Method
To solve a linear equation using this method, we add, subtract, multiply, or divide both sides of the
equation by the same number.
Transposing a number (i e. . changing the side of the number) is the same as adding or subtracting the
number from both sides of the equation. In doing so, we change the sign of the number.

EXAMPLE 1. Solve : 2m - 12 = 18.

SOLUTION : By Systematic Method By Transposing
2m - 12 = 18 2m - 12 = 18

2m - 12 12+ = 18 12+ 2m = 18 12+
(By adding 12 on both sides) (On transposing -12, it becomes + 12)
2m = 30 2m = 30
2m 30 30
= m =
2 2 2

(Dividing both sides by 2) (On transposing ‘multiplication’ it becomes
‘division’ on RHS)
m = 15
\ m = 15

EX AM PLE 2. Solve the equa tion 8 + x = 3 and check the re sult.
SOLUTION : 8 + x = 3

Þ 8 + x – 8 = 3 – 8 [Subtracting 8 from both sides]
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