Question 1:
Solve the linear equation : x/2 - 1/5 = x/3 + 1/4
Answer:
x/2 - 1/5 = x/3 + 1/4
L.C.M. of the denominators, 2, 3, 4, and 5, is 60.
Multiplying both sides by 60, we obtain
60 ( x/2 - 1/5 ) = ( x/3 + 1/4 )
⇒ 30x − 12 = 20x + 15 (Opening the brackets)
⇒ 30x − 20x = 15 + 12
⇒ 10x = 27
⇒ x = 27/10
Question 2:
Solve the linear equation: n/2 - 3n/4 + 5n/6 = 21
Answer:
n/2 - 3n/4 + 5n/6 = 21
L.C.M. of the denominators, 2, 4, and 6, is 12.
Multiplying both sides by 12, we obtain
6n − 9n + 10n = 252
⇒ 7n = 252
⇒ n = 36
Question 3:
Solve the linear equation: x + 7 - 8x/3 = 17/6 + 5x/2
Answer:
x + 7 - 8x/3 = 17/6 + 5x/2
L.C.M. of the denominators, 2, 3, and 6, is 6.
Multiplying both sides by 6, we obtain
6x + 42 − 16x = 17 − 15x
⇒ 6x − 16x + 15x = 17 − 42
⇒ 5x = −25
⇒ x = −5
Question 4:
Solve the linear equation: ( x - 5 )/3 = ( x - 3 )/5
Answer:
L.C.M. of the denominators, 3 and 5, is 15.
Multiplying both sides by 15, we obtain
5 ( x − 5 ) = 3 ( x − 3 )
⇒ 5x − 25 = 3x − 9 (Opening the brackets)
⇒ 5x − 3x = 25 − 9
⇒ 2x = 16
⇒ x = 8
Question 5:
Solve the linear equation: ( 3t - 2 )/4 - ( 2t + 3 )/3 = 2/3 - t
Answer:
L.C.M. of the denominators, 3 and 4, is 12.
Multiplying both sides by 12, we obtain
3 ( 3t − 2 ) − 4 ( 2t + 3 ) = 8 − 12t
⇒ 9t − 6 − 8t − 12 = 8 − 12t (Opening the brackets)
⇒ 9t − 8t + 12t = 8 + 6 + 12
⇒ 13t = 26
⇒ t = 2
Question 6:
Solve the linear equation : m - ( m - 1 )/2 = 1 - ( m - 2 )/3
Answer:
m- ( m - 1 )/2 =1 - ( m - 2 )/3
L.C.M. of the denominators, 2 and 3, is 6.
Multiplying both sides by 6, we obtain
6m − 3 ( m − 1 ) = 6 − 2 ( m − 2 )
⇒ 6m − 3m + 3 = 6 − 2m + 4 (Opening the brackets)
⇒ 6m − 3m + 2m = 6 + 4 − 3
⇒ 5m = 7
⇒ m = 7/5
Question 7:
Simplify and solve the linear equation: 3( t − 3 ) = 5 ( 2t + 1 )
Answer:
3 ( t − 3 ) = 5 ( 2t + 1 )
⇒ 3t − 9 = 10t + 5 (Opening the brackets)
⇒ −9 − 5 = 10t − 3t
⇒ −14 = 7t
⇒ t = -7
Question 8:
Simplify and solve the linear equation: 15 ( y − 4 ) − 2 ( y − 9 ) + 5 ( y + 6 ) = 0
Answer:
15(y − 4) − 2(y − 9) + 5(y + 6) = 0
⇒ 15y − 60 − 2y + 18 + 5y + 30 = 0 (Opening the brackets)
⇒ 18y − 12 = 0
⇒ 18y = 12
⇒ y = 2/3
Question 9:
Simplify and solve the linear equation: 3 ( 5z − 7 ) − 2 ( 9z − 11 ) = 4 ( 8z − 13 ) − 17
Answer:
3(5z − 7) − 2(9z − 11) = 4(8z − 13)−17
⇒ 15z − 21 − 18z + 22 = 32z − 52 − 17 (Opening the brackets)
⇒ −3z + 1 = 32z − 69
⇒ −3z − 32z = −69 − 1
⇒ −35z = −70
⇒ z = 2
Question 10:
Simplify and solve the linear equation: 0.25 ( 4f − 3 ) = 0.05 ( 10f − 9 )
Answer:
0.25 ( 4f − 3 ) = 0.05 ( 10f − 9)
Multiplying both sides by 20, we obtain
5 ( 4f − 3 ) = 10f − 9
⇒ 20f − 15 = 10f − 9 (Opening the brackets)
⇒ 20f − 10f = − 9 + 15
⇒ 10f = 6
⇒ f = 0.6
Solve the linear equation : x/2 - 1/5 = x/3 + 1/4
Answer:
x/2 - 1/5 = x/3 + 1/4
L.C.M. of the denominators, 2, 3, 4, and 5, is 60.
Multiplying both sides by 60, we obtain
60 ( x/2 - 1/5 ) = ( x/3 + 1/4 )
⇒ 30x − 12 = 20x + 15 (Opening the brackets)
⇒ 30x − 20x = 15 + 12
⇒ 10x = 27
⇒ x = 27/10
Question 2:
Solve the linear equation: n/2 - 3n/4 + 5n/6 = 21
Answer:
n/2 - 3n/4 + 5n/6 = 21
L.C.M. of the denominators, 2, 4, and 6, is 12.
Multiplying both sides by 12, we obtain
6n − 9n + 10n = 252
⇒ 7n = 252
⇒ n = 36
Question 3:
Solve the linear equation: x + 7 - 8x/3 = 17/6 + 5x/2
Answer:
x + 7 - 8x/3 = 17/6 + 5x/2
L.C.M. of the denominators, 2, 3, and 6, is 6.
Multiplying both sides by 6, we obtain
6x + 42 − 16x = 17 − 15x
⇒ 6x − 16x + 15x = 17 − 42
⇒ 5x = −25
⇒ x = −5
Question 4:
Solve the linear equation: ( x - 5 )/3 = ( x - 3 )/5
Answer:
L.C.M. of the denominators, 3 and 5, is 15.
Multiplying both sides by 15, we obtain
5 ( x − 5 ) = 3 ( x − 3 )
⇒ 5x − 25 = 3x − 9 (Opening the brackets)
⇒ 5x − 3x = 25 − 9
⇒ 2x = 16
⇒ x = 8
Question 5:
Solve the linear equation: ( 3t - 2 )/4 - ( 2t + 3 )/3 = 2/3 - t
Answer:
L.C.M. of the denominators, 3 and 4, is 12.
Multiplying both sides by 12, we obtain
3 ( 3t − 2 ) − 4 ( 2t + 3 ) = 8 − 12t
⇒ 9t − 6 − 8t − 12 = 8 − 12t (Opening the brackets)
⇒ 9t − 8t + 12t = 8 + 6 + 12
⇒ 13t = 26
⇒ t = 2
Question 6:
Solve the linear equation : m - ( m - 1 )/2 = 1 - ( m - 2 )/3
Answer:
m- ( m - 1 )/2 =1 - ( m - 2 )/3
L.C.M. of the denominators, 2 and 3, is 6.
Multiplying both sides by 6, we obtain
6m − 3 ( m − 1 ) = 6 − 2 ( m − 2 )
⇒ 6m − 3m + 3 = 6 − 2m + 4 (Opening the brackets)
⇒ 6m − 3m + 2m = 6 + 4 − 3
⇒ 5m = 7
⇒ m = 7/5
Question 7:
Simplify and solve the linear equation: 3( t − 3 ) = 5 ( 2t + 1 )
Answer:
3 ( t − 3 ) = 5 ( 2t + 1 )
⇒ 3t − 9 = 10t + 5 (Opening the brackets)
⇒ −9 − 5 = 10t − 3t
⇒ −14 = 7t
⇒ t = -7
Question 8:
Simplify and solve the linear equation: 15 ( y − 4 ) − 2 ( y − 9 ) + 5 ( y + 6 ) = 0
Answer:
15(y − 4) − 2(y − 9) + 5(y + 6) = 0
⇒ 15y − 60 − 2y + 18 + 5y + 30 = 0 (Opening the brackets)
⇒ 18y − 12 = 0
⇒ 18y = 12
⇒ y = 2/3
Question 9:
Simplify and solve the linear equation: 3 ( 5z − 7 ) − 2 ( 9z − 11 ) = 4 ( 8z − 13 ) − 17
Answer:
3(5z − 7) − 2(9z − 11) = 4(8z − 13)−17
⇒ 15z − 21 − 18z + 22 = 32z − 52 − 17 (Opening the brackets)
⇒ −3z + 1 = 32z − 69
⇒ −3z − 32z = −69 − 1
⇒ −35z = −70
⇒ z = 2
Question 10:
Simplify and solve the linear equation: 0.25 ( 4f − 3 ) = 0.05 ( 10f − 9 )
Answer:
0.25 ( 4f − 3 ) = 0.05 ( 10f − 9)
Multiplying both sides by 20, we obtain
5 ( 4f − 3 ) = 10f − 9
⇒ 20f − 15 = 10f − 9 (Opening the brackets)
⇒ 20f − 10f = − 9 + 15
⇒ 10f = 6
⇒ f = 0.6
