Solve: 5 x - 4 6 = 4 x + 1 - 3 x + 10 2

We have, 5 x - 4 6 = 4 x + 1 - 3 x + 10 2 Taking LCM of 1 and 2 = 2 on RHS 5 x - 4 6 = 2 ( 4 x + 1 ) - 3 x - 10 2 5 x - 4 6 = 8 x + 2 - 3 x - 10 2 5 x - 4 6 = 5 x - 8 2 By cross multiplication we get, 2 ( 5 x - 4 ) = 6 ( 5 x - 8 ) ⇒ 10 x - 8 = 30 x - 48 ⇒ 10 x - 30 x = - 48 + 8 ⇒ - 20 x = - 40 Dividing both the sides by - 20 we get, ⇒ x = 2 Therefore, x = 2

Solve: 5 x - 4 6 = 4 x + 1 - 3 x + 10 2

We have, 5 x - 4 6 = 4 x + 1 - 3 x + 10 2 Taking LCM of 1 and 2 = 2 on RHS 5 x - 4 6 = 2 ( 4 x + 1 ) - 3 x - 10 2 5 x - 4 6 = 8 x + 2 - 3 x - 10 2 5 x - 4 6 = 5 x - 8 2 By cross multiplication we get, 2 ( 5 x - 4 ) = 6 ( 5 x - 8 ) ⇒ 10 x - 8 = 30 x - 48 ⇒ 10 x - 30 x = - 48 + 8 ⇒ - 20 x = - 40 Dividing both the sides by - 20 we get, ⇒ x = 2 Therefore, x = 2

Solve: 5 x - 1 3 ( x + 1 ) = 6 x + 1 30

We have, 5 x - 1 3 ( x + 1 ) = 6 x + 1 30 5 x - x + 1 3 = 6 x + 1 30 Taking LCM on both the sides we get, 15 x - ( x + 1 ) 3 = 6 ( 30 x + 1 ) 30 By cross multiplication, ⇒ 10 ( 14 x - 1 ) = 6 ( 30 x + 1 ) ⇒ 140 x - 180 x = 6 + 10 ⇒ - 40 x = 16 ⇒ x = - 2 5 Therefore, x = - 2 5

Solve: 4 - 2 ( z - 4 ) 3 = 1 2 ( 2 z + 5 )

We have, 4 - 2 ( z - 4 ) 3 = 1 2 ( 2 z + 5 ) Taking LCM of 1 and 3 = 3 on LHS 12 - 2 ( z - 4 ) 3 = 2 z + 5 2 By cross multiplication ⇒ 2 ( 12 - 2 z + 8 ) = 3 ( 2 z + 5 ) ⇒ 40 - 4 z = 6 z + 15 ⇒ - 4 z - 6 z = 15 - 40 ⇒ - 10 z = - 25 ⇒ z = - 25 - 10 = 5 2 Therefore, z = 5 2

Solve: 3 ( y - 5 ) 4 - 4 y = 3 - ( y - 3 ) 2

We have, 3 ( y - 5 ) 4 - 4 y = 3 - ( y - 3 ) 2 Taking LCM of 4 and 1 on LHS = 4 and LCM of 1 and 2 on RHS = 2 ⇒ 3 ( y - 5 ) - 16 y 4 = 6 - y + 3 2 ⇒ 3 y - 15 - 16 y 4 = 9 - y 2 By cross multiplication ⇒ - 13 y - 15 = 4 ( 9 - y ) 2 ⇒ - 13 y - 15 = 2 ( 9 - y ) ⇒ - 13 y - 15 = 18 - 2 y ⇒ - 13 y + 2 y = 18 + 15 ⇒ - 11 y = 33 Dividing both the sides by - 11 we get, ⇒ y = - 3 Therefore, y = - 3

Solve: 8 x - 3 3 x = 2

We have, 8 x - 3 3 x = 2 By cross multiplication ⇒ 8 x - 3 = 6 x ⇒ 8 x - 6 x = 3 ⇒ 2 x = 3 ⇒ x = 3 2 Therefore, x = 3 2

Solve: 9 x 7 - 6 x = 15

We have, 9 x 7 - 6 x = 15 By cross multiplication ⇒ 9 x = 15 ( 7 - 6 x ) ⇒ 9 x = 105 - 90 x ⇒ 9 x + 90 x = 105 ⇒ 99 x = 105 ⇒ x = 105 99 = 35 33 Therefore, x = 35 33

Solve: 3 x 5 x + 2 = - 4

We have, 3 x 5 x + 2 = - 4 By cross multiplication ⇒ 3 x = - 4 ( 5 x + 2 ) ⇒ 3 x = - 20 x - 8 ⇒ 3 x + 20 x = - 8 ⇒ 23 x = - 8 ⇒ x = - 8 23 Therefore, x = - 8 23

Solve: 6 y - 5 2 y = 7 9

We have, 6 y - 5 2 y = 7 9 By cross multiplication ⇒ 9 ( 6 y - 5 ) = 14 y ⇒ 54 y - 45 = 14 y ⇒ 54 y - 14 y = 45 ⇒ 40 y = 45 ⇒ y = 45 40 = 9 8 Therefore, y = 9 8

Solve: 2 - 9 z 17 - 4 z = 4 5

We have, 2 - 9 z 17 - 4 z = 4 5 By cross multiplication ⇒ 5 ( 2 - 9 z ) = 4 ( 17 - 4 z ) ⇒ 10 - 45 z = 68 - 16 z ⇒ - 45 z + 16 z = 68 - 10 ⇒ - 29 z = 58 ⇒ z = 58 - 29 = - 2 Therefore, z = - 2