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4.2.1 Linear Equations I, PT3 Practice 1

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4.2.1 Linear Equations I, PT3 Practice 1
Question 1:
Solve the following linear equations.
  (a)  4 – 3n = 5n – 4   
  (b) 4 m − 2 10 + m = 1 2  

Solution:
(a)
4 – 3n = 5n – 4   
–3n –5n = – 4 – 4   
–8n = – 8   
 8n = 8
n = 8/8 = 1
 
(b) 4 m − 2 10 + m = 1 2 2 ( 4 m − 2 ) = 10 + m 8 m − 4 = 10 + m 8 m − m = 10 + 4 7 m = 14 m = 14 7 m = 2


Question 2:
Solve the following linear equations.
(a) x 3 = 4 − x (b) 3 ( x − 2 ) 5 = 9
 
Solution:
(a) x 3 = 4 − x x = 3 ( 4 − x ) x = 12 − 3 x x + 3 x = 12 4 x = 12 x = 12 4 x = 3

(b) 3 ( x − 2 ) 5 = 9 3 ( x − 2 ) = 9 × 5 3 x − 6 = 45 3 x = 45 + 6 3 x = 51 x = 51 3 x = 17



Question 3:
Solve the following linear equations.
(a) 3 m 4 + 15 = 9 (b) 2 m + 8 = 3 ( m − 2 )

Solution:
(a) 3 m 4 + 15 = 9 3 m 4 = 9 − 15 3 m 4 = − 6 3 m = − 6 × 4 3 m = − 24 m = − 24 3 m = − 8
 
(b) 2 m + 8 = 3 ( m − 2 ) 2 m + 8 = 3 m − 6 2 m − 3 m = − 6 − 8 − m = − 14 m = 14


Question 4:
Solve the following linear equations.
(a) 11 + 2 x 3 = 9 (b) x − 5 3 = x 6

Solution:
(a) 11 + 2 x 3 = 9 2 x 3 = 9 − 11 2 x 3 = − 2 2 x = − 6 x = − 6 2 x = − 3
 
(b) x − 5 3 = x 6 6 ( x − 5 ) = 3 x 6 x − 30 = 3 x 6 x − 3 x = 30 3 x = 30 x = 10


Question 5:
Solve the following linear equations.
(a) 4 ( 2 x − 3 ) = 24 (b) y 2 − y + 4 3 = 5

Solution:
(a) 4 ( 2 x − 3 ) = 24 8 x − 12 = 24 8 x = 24 + 12 8 x = 36 x = 36 8 x = 4 1 2
 
(b) y 2 − y + 4 3 = 5 y × 3 2 × 3 − 2 ( y + 4 ) 3 × 2 = 5 3 y − 2 ( y + 4 ) 6 = 5 3 y − 2 y − 8 = 30 y = 30 + 8 y = 38