Page 104 - Maths Skills - 8

102 Maths

3. Solve the following equations.

3x 15 1 1
(i) 3 (ii) 1 1 4
2
2x x x

x 1 x 2 x 5 x 5x 4 3x 10
(iii) (iv) 4x
1
2 3 4 12 6 2
1 x 04. y 4
(v) 5 (vi) 1
3
x 03. y 3
3
y 7 2x ( 7 5x ) 7
(vii) 4 5 (viii)
2 y 4 4 9x ( 3 4x) 6
5
(ix) (x + 3) – (x + 2) = 5 (x) x(x + 1) – x(x + 2) + 3x = 6
2
2
3x 4 6x 2 x ( x 1) ( x 2)

2
(xi) (xii) 6
2x 6 4x x 5 1
6
APPLICATIONS OF LINEAR EQUATIONS IN ONE VARIABLE
Application of linear equations to practical problems can be solved by forming an equation with the condition
given in the problem and then solving it in the usual manner.

Let’s Attempt

Example 1: The sum of three consecutive numbers is 15. Find the numbers.
Solution: Let the first number be x. Then, the three consecutive numbers will be

x, (x + 1), and (x + 2). Fact-o-meter
According to the given condition,
x + (x + 1) + (x + 2) = 15 � Consecutive numbers are taken
as: (x + 1), (x + 2), (x + 3) .....
⇒ 3x + 3 = 15 � Consecutive even numbers are

⇒ 3x = 12 taken as: x, x + 2, x + 4 .....
� Consecutive odd numbers are
12
⇒ x = taken as: x, x + 2, x + 4 .....
3 � Consecutive multiple of 4 are
x = 4 taken as: x, x + 4, x + 8 .....

Hence, the three consecutive numbers are x = 4, x + 1 = 4 + 1 = 5, and x + 2 = 4 + 2 = 6.

Example 2: The sum of the digits of a two-digit number is 7. The number obtained by interchanging the digits
exceeds the original number by 27. Find the original number.

Solution: It is given that the sum of the digits of a two-digit number is 7, and the number obtained by
interchanging the digits exceeds the original number by 27. Let x be at ones place of the two-digit
number. Then, (7 – x) is the digit at the tens place.