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Solve the following equations. 1. (8x – 3)/3x = 2 2. 9x/(7 – 6x) = 15 3. z/(z + 15) = 4/9

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Solve the following equations.

1. (8x – 3)/3x = 2

2. 9x/(7 – 6x) = 15

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

4. (3y + 4)/(2 – 6y) = -2/5

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

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1. (8x – 3)/3x = 2

(8x – 3)/3x = 2

⇒ 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

9x/(7 – 6x) = 15

⇒ 9x = 15(7 – 6x)

⇒ 9x = 105 – 90x

⇒ 9x + 90x = 105

⇒ 99x = 105

⇒ x = 105/99

= 35/33

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

z/(z + 15) = 4/9

⇒ 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

(3y + 4)/(2 – 6y) = -2/5

⇒ 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

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

⇒ 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

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