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4.2.2 Linear Equations I, PT3 Practice

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Question 6:
Solve each of the following equations:
(a)  5 a − 16 = a (b)  6 + 2 3 ( − 9 p + 12 ) = p


Solution:
(a)
5 a − 16 = a 5 a − a = 16 4 a = 16 a = 4

(b)
6 + 2 3 ( − 9 p + 12 ) = p 6 − 6 p + 8 = p − 6 p − p = − 8 − 6 − 7 p = − 14 p = 2


Question 7::
Solve each of the following equations:
(a)  a − 2 = a 5 (b)  b − 3 4 = 2 + b 5

Solution:
(a)
a − 2 = a 5 5 a − 2 = a 4 a = 2 a = 2

(b)
b − 3 4 = 2 + b 5 5 b − 15 = 8 + 4 b 5 b − 4 b = 8 + 15 b = 23

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Question 8:
Solve each of the following equations:
(a)  x = − 24 − x (b)  y + 5 4 ( 4 − 2 y ) = − 4

Solution:
(a)
x = − 24 − x 2 x = − 24 x = − 12

(b)
y + 5 4 ( 4 − 2 y ) = − 4 4 y + 20 − 10 y = − 16    ( × 4 ) − 6 y = − 16 − 20 − 6 y = − 36 y = 6


Question 9:
Solve each of the following equations:
(a)  5 p = 8 p − 9 (b)  3 q = 20 − 13 q 4

Solution:
(a)
5 p = 8 p − 9 5 p − 8 p = − 9 − 3 p = − 9 p = 3

(b)
3 q = 20 − 13 q 4 12 q = 20 − 13 q 12 q + 13 q = 20 25 q = 20 q = 4 5