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