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**EXERCISE 2.6**

**Question: **Solve the following equations

1.

2.

3.

4.

5.

**Solution: **

1.

Multiplying both sides by 3x, we have

or

8x â€“ 3 = 6x

Transposing (â€“3) to RHS and 6x to LHS, we have

8x â€“ 6x = 3

or

2x = 3

Dividing both sides by 2, we have

x = 3/2

**2.**

Multiplying both sides by 7 â€“ 6x, we have

or

9x = 105 â€“ 90x

Transposing (â€“90x) to LHS, we have

9x + 90x = 105

or

99x = 105

or

x = 105/99 (Dividing both sides by 99)

or

x = 35/33

**3.**

By cross multiplication, we have

9z = 4(z + 15) â‡’ 9z = 4z + 60

Transposing 4z to LHS, we have

9z â€“ 4z = 60

5z = 60 â‡’ z = 60/5 = 12

âˆ´ z = 12

**4.**

By cross multiplication, we have

5(3y + 4) = â€“2(2 â€“ 6y)

or

15y + 20 = â€“4 + 12y

Transposing 20 to RHS and 12y to LHS, we have

15y â€“ 12y = â€“4 â€“ 20

or

3y = â€“24

or

y = - 24/3= â€“8 (Dividing both sides by 3)

or y = â€“8

**5.**

By cross multiplication, we have

3 * [7y + 4] = â€“4 x [y + 2]

or

21y + 12 = â€“4y â€“ 8

Transposing 12 to RHS and (â€“4y) to LHS, we have

21y + 4y = â€“8 â€“ 12

or

25y = â€“20

or

y = -20/25 (Dividing both sides by 25)

or

y = -20/25 = -4

âˆ´ 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.****Solution:** Let the present age of Hari = 5x years

and the present age of Harry = 7x years

After 4 years, Age of Hari = (5x + 4) years

Age of Harry = (7x + 4) years

According to the condition,

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

or

By cross multiplication, we have:

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

or

20x + 16 = 21x + 12

Transposing 16 to RHS and 21x to LHS, we have

20x â€“ 21x = 12 â€“ 16

â€“x = â€“4 â‡’ x = 4

âˆ´ Present age of Hari = 5 * 4 = 20 years

Present age of Harry = 7 * 4 = 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. Findthe rational number.****Solution: **Let the numerator = x

âˆ´ Denominator = x + 8

New numerator = (x) + 17

New denominator = (x + 8) â€“ 1 = x + 7

âˆ´ The new number =

According to the condition, we have

By cross multiplication, we have

2(x + 17) = 3(x + 7) 2x + 3x = 3x + 21

Transposing 34 to RHS and 3x to LHS, we have

2x â€“ 34 = 21 â€“ 34 â‡’ â€“x = â€“13

âˆ´ x= 13 â‡’ Numerator = 13

x + 8 = 13 + 8 = 21 â‡’Denominator = 21

âˆ´ The rational number = 13/21

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