**Solve the following equations**.

**1. (8x – 3)/3x = 2**

**Solution:**

Given, (8x – 3)/3x = 2

Now,

8x/3x – 3/3x = 2

8/3 – 1/x = 2

8/3 – 2 = 1/x

(8 – 6)/3 = 1/x

2/3 = 1/x

x = 3/2

**2. 9x/(7 – 6x) = 15**

**Solution:**

Given, 9x/(7 – 6x) = 15

Now,

9x = 15(7 – 6x)

9x = 105 – 90x

9x + 90x = 105

99x = 105

x = 105/99 = 35/33

**3. z/(z + 15) = 4/9**

**Solution:**

Given, z/(z + 15) = 4/9

Now,

z = 4/9 (z + 15)

9z = 4(z + 15)

9z = 4z + 60

9z – 4z = 60

5z = 60

z = 12

**4. (3y + 4)/(2 – 6y) = -2/5**

**Solution:**

Given, (3y + 4)/(2 – 6y) = -2/5

Now,

3y + 4 = -2/5 (2 – 6y)

5(3y + 4) = -2(2 – 6y)

15y + 20 = -4 + 12y

15y – 12y = -4 – 20

3y = -24

y = -8

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

**Solution:**

Given, (7y + 4)/(y + 2) = -4/3

Now,

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

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

21y + 12 = -4y – 8

21y + 4y = -8 – 12

25y = -20

y = -20/25 = -4/5

**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 us assume the age of Hari be 5x and Harry be 7x.

After 4 years,

Age of Hari = 5x + 4

Age of Harry = 7x + 4

According to the question,

(5x + 4)/(7x + 4) = ¾

⇒ 4(5x + 4) = 3(7x + 4)

⇒ 20x + 16 = 21x + 12

⇒ 21x – 20x = 16 – 12

⇒ x = 4

Hence,

Hari age = 5x = 5 × 4 = 20 years

Harry age = 7x = 7 × 4 = 28 years

**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.**

**Solution:**

Let us assume the numerator be x then denominator will be (x + 8)

According to the question,

(x + 17)/(x + 8 – 1) = 3/2

⇒ (x + 17)/(x + 7) = 3/2

⇒ 2(x + 17) = 3(x + 7)

⇒ 2x + 34 = 3x + 21

⇒ 34 – 21 = 3x – 2x

⇒ 13 = x

Hence, the rational number is x/(x + 8) = 13/21

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