## Chapter 2 Linear Equations in One Variable Exercise 2.6

**Solve the following equations.**

Question 1: (8x - 3)/3x = 2

Answer:

Question 1: (8x - 3)/3x = 2

Answer:

= 8x - 3 = 2 × 3x

= 8x - 3 = 6x

= 8x - 6x = 3

= 2x = 3

= x = 3/2

**Question 2: 9x/(7 - 6x) = 15**

Answer:

Answer:

= 9x/7 - 6x = 15/1

= 9x = 105 - 90x

= 99x = 105

= x = 105/99

= x = 35/33

**Question 3: z/(z + 15) = 4/9**

Answer:

Answer:

= 9z = 4z + 60

= 9z - 4z = 60

= 5z = 60

= z = 60/5

= z = 12

**Question 4: (3y + 4)/(2 - 6y) = -2/5**

Answer:

Answer:

= 15y + 20 = -4 - (12y)

= 15y - 12ty = -4 - 20

= 3y = -24

= y = -24/3

= y = -8

**Question 5: (7y + 4)/(y + 2) = -4/3**

Answer:

Answer:

= -4(y + 2) = 3(7y + 4)

= -4y - 8 = 21y + 12

= -4y - 21y = 12 + 8

= -25y = 20

= y = 20/-25

= y = -4/5

**Question 6: The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.**

Answer:

Answer:

Let the present age of Hari and Harry be 5x and 7x.

After 4 years, Hari’s age = (5x + 4) years

After 4 years, Harry’s age = (7x + 4) years

= 5x + 4/7x + 4

= 5x + 4/7x + 4 = 3/4

= 4(5x + 4) = 3(7x + 4)

= 20x + 16 = 21x + 12

= 20x - 21x = 12 - 16

= -1x = -4

= 1x = 4

= x = 4

Hari's age = 5x = 5 × 4 = 20

Harry's age = 7x = 7 × 4 = 28

Therefore, the present age of Hari is 20 years, while the present age of Harry is 28 years.

**Question 7: The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.**

Answer:

Answer:

Let the numerator be x, denominator be x + 8.

Given

= x + 17/x + 8 - 1 = 3/2

= x + 17/x + 7 = 3/2

= 2(x + 17) = 3(x + 7)

= 2x + 34 = 3x + 21

= 2x - 3x = 21 - 34

= -1x = -13

= 1x = 13

= x = 13

Rational number

= x/x + 8

= 13/13 + 8

= 13/21

Therefore, the rational number is 13/21.

Wow

ReplyDelete