# Linear Equations in One Variable : Exercise 2.6 (Mathematics NCERT Class 8th)

**Solve the following linear equations.**

**Q.1 **

** Sol.** Given,

Multiplying by 3

*x*on both the sides, we get,

(8x - 3) = 2 X 3x

(8x - 3) = 6x

8x - 6x = 3

2x = 3

**Q.2 **

** Sol.** Given,

Multiplying by (7 â€“ 6

*x*) on both the sides, we get,

9x = 15 (7 - 6x)

9x =105 -90x

9x +90x = 105

99x =105

**Q.3 **

** Sol.** Given,

Multiplying by 9(

*z*+ 15) on both the sides, we get,

9z = 4 (z + 15)

9z = 4z +60

9z - 4z = 60

5z = 60

z=15

**Q.4 **

** Sol.** Given,

Multiplying by 5(2 â€“ 6

*y*) on both the sides, we get,

5(3y + 4) = -2 (2 - 6y)

15y + 20 = -4 + 12y

15y - 12y = -4 -20

3y = -24

y = -8

**Q.5 **

** Sol.** Given,

Multiplying by 3(

*y*+ 2) on both the sides, we get,

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

21y + 12 = -4y - 8

21y + 4y = -8-12

25y = -20

**Q.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.
**

**Let the ages of Hari and Harry be 5**

*Sol.**x*and 7

*x*respectively.

After 4 years, the ages of Hari and Harry will be (5

*x*+ 4) and (7

*x*+ 4) respectively.

Given,

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

20x +16 = 21x + 12

20 - 21x =12 - 16

-x = -4

x = 4

Therefore, age of Hari = 5

*x*= 5 x 4 = 20

Age of Harry = 7

*x*= 7 x 4 = 28

Thus, the present ages of Hari and Harry are 20 and 28 years respectively.

**Q.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 . Find the rational number.
**

**Let the numerator of a rational number be a. Thus, denominator will be a + 8.**

*Sol.*Therefore, rational number will be

Given,

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

2a + 34 = 3a + 21

2a - 3a = 21 - 34

-a = -13

a = 13

Thus, the required rational is

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