Chapter 4: Linear Equations in One Variable

Solution:-

(b) 1/15

Given,

1/3 + S = 2/5

S = 2/5 – 1/3

S = (6 – 5)/15

S = 1/15

Solution:-

(c) (¾)²

Given,

(-4/3)y = -¾

Y = – ¾ × -¾

Y = 9/16

Y = (3 × 3)/(4 × 4)

Y = 3²/4²

Y = (¾)²

Solution:-

(a) 11b + 30

From the question it is given that,

Let the digit at units place be b.

The digit in the tens place of a two digit number is 3 more than the digit in the units place = 3 + b

So, the number = 10 (3 + b) + b

= 30 + 10b + b

= 30 + 11b

Solution:-

(d) 3(x + 3)

Given,

Shilpa’s age three years ago was x

Then, Shilpa’s present age is = x + 3

Arpita’s present age is thrice of Shilpa = 3 (x + 3)

Solution:-

(a) 112

Let us assume the three consecutive multiples of 7 be 7x, (7x + 7), (7x + 14), where x is a natural number.

As per the condition in the question,

7x + (7x + 7) + (7x + 14) = 357

21x + 21 = 357

21(x + 1) = 357

(21(x + 1))/21 = 357/21

X + 1 = 17

X = 17 – 1

X = 16

Therefore, the smallest multiple of 7 is,

7 × 16 = 112.

In questions 16 to 32, fill in the blanks to make each statement true.

Solution:-

In a linear equation, the highest power of the variable appearing in the equation is one.

Solution:-

The solution of the equation 3x – 4 = 1 – 2 x is 1.

3x – 4 = 1 – 2

3x – 4 = – 1

3x = -1 + 4

X = 3/3

X = 1

Solution:-

The solution of the equation 2y = 5y – 18 5 is (6/5).

2y = 5y – (18/5)

(18/5) = 5y – 2y

(18/5) = 3y

y = (18/5) × (1/3)

y = (6/5) × (1/1)

y = 6/5

Solution:-

Any value of the variable which makes both sides of an equation equal is known as a solution of the equation.

Solution:-

9x – 3 = –21 has the solution (–2)

In the question it is given that, x = -2

Then, let us assume the missing number be y

(9 × (-2)) – y = -21

-18 – y = -21

– y = -21 + 18

– y = – 3

Y = 3