Solve the following equation. x 3 - x 4 = 14

Given equation: x 3 - x 4 = 14 ⇒ 4 x - 3 x 12 = 14 ( LCM of 3 and 4 is 12 ) x 12 = 14 x 12 × 12 = 14 × 12 (Multiplying by 12 on both sides) ⇒ x = 12 × 14 x = 168 ∴ The solution of the given equation is x = 168 .

Solve the following equation. x 3 - x 4 = 14

Given equation: x 3 - x 4 = 14 ⇒ 4 x - 3 x 12 = 14 ( LCM of 3 and 4 is 12 ) x 12 = 14 x 12 × 12 = 14 × 12 (Multiplying by 12 on both sides) ⇒ x = 12 × 14 x = 168 ∴ The solution of the given equation is x = 168 .

Solve the following equation. z 2 + z 3 - z 6 = 8

Given equation: z 2 + z 3 - z 6 = 8 ⇒ 3 z + 2 z - z 6 = 8 ( LCM of 2 , 3 and 6 is 6 ) 4 z 6 = 8 ⇒ 4 z = 8 × 6 (Transposing 6 to RHS ) 4 z = 48 ⇒ z = 48 4 (Transposing 4 to RHS ) z = 12 ∴ The solution of the given equation is z = 12 .

Solve the following equation. 2 p 3 - p 5 = 11 2 3

Given equation: 2 p 3 - p 5 = 11 2 3 2 p 3 - p 5 = 35 3 (Convert mixed fraction into improper fraction) ⇒ 10 p - 3 p 15 = 35 3 ( LCM of 3 and 5 is 15 ) ⇒ 7 p 15 × 15 = 35 3 × 15 (Multiplying by 15 on both sides) 7 p = 175 7 p 7 = 175 7 (Dividing by 7 on both sides) ⇒ p = 175 7 p = 25 ∴ The solution of the given equation is p = 25 .

Solve the following equation. 9 1 4 = y - 1 1 3

Given equation: 9 1 4 = y - 1 1 3 37 4 = y - 4 3 (Convert mixed fraction into improper fraction) ⇒ 37 4 + 4 3 = y (Transposing 4 3 to RHS ) ⇒ 111 + 16 12 = y ( LCM of 3 and 4 is 12 ) y = 127 12 ∴ The solution of the given equation is y = 127 12 .

Solve the following equation. x 2 - 4 5 + x 5 + 3 x 10 = 1 5

Given equation: x 2 - 4 5 + x 5 + 3 x 10 = 1 5 ⇒ x 2 + x 5 + 3 x 10 = 1 5 + 4 5 (Transposing 4 5 to RHS ) ⇒ 5 x + 2 x + 3 x 10 = 4 + 1 5 ( LCM of 2 , 5 and 10 is 10 ) 10 x 10 = 5 5 ∴ x = 1 ∴ The solution of the given equation is x = 1 .

Solve the following equation. x 2 - 1 4 = x 3 + 1 2

Given equation: x 2 - 1 4 = x 3 + 1 2 ⇒ x 2 - x 3 = 1 2 + 1 4 (Transposing x 3 to LHS and 1 4 to RHS ) 3 x - 2 x 6 = 2 + 1 4 ( LCM of 2 and 3 is 6 and of 2 and 4 is 4 ) x 6 = 3 4 ⇒ x = 3 4 × 6 ( Transpose 6 to R H S ) x = 9 2 ∴ The solution of the given equation is x = 9 2 .

Solve the following equation. 2 x - 3 3 x + 2 = - 2 3

Given equation: 2 x - 3 3 x + 2 = - 2 3 Multiplying ( 3 x + 2 ) and 3 on both sides, we get 2 x - 3 3 x + 2 × ( 3 x + 2 ) × 3 = - 2 3 × ( 3 x + 2 ) × 3 3 ( 2 x - 3 ) = - 2 ( 3 x + 2 ) On solving further, ⇒ 6 x - 9 = - 6 x - 4 (Removing brackets) ⇒ 6 x + 6 x = - 4 + 9 (Transposing 6 x to LHS and 9 to RHS ) 12 x = 5 ⇒ x = 5 12 (Transposing 12 to RHS ) ∴ The solution of the given equation is x = 5 12 .

Solve the following equation. 8 p - 5 7 p + 1 = - 2 4

Given equation: 8 p - 5 7 p + 1 = - 2 4 Multiplying ( 7 p + 1 ) and 4 on both sides, we get 8 p - 5 7 p + 1 × ( 7 p + 1 ) × 4 = - 2 4 × ( 7 p + 1 ) × 4 4 ( 8 p - 5 ) = - 2 ( 7 p + 1 ) On further solving, ⇒ 32 p - 20 = - 14 p - 2 (Removing brackets) ⇒ 32 p + 14 p = - 2 + 20 (Transposing 14 p to LHS and 20 to RHS ) 46 p = 18 ⇒ p = 18 46 (Transposing 46 to RHS ) p = 9 23 ∴ The solution of the given equation is p = 9 23 .

Solve the following equation. 7 y + 2 5 = 6 y - 5 11

Given equation: 7 y + 2 5 = 6 y - 5 11 LCM of 5 and 11 is 55 . ⇒ 7 y + 2 5 × 55 = 6 y - 5 11 × 55 (Multiplying by 55 on both sides) 11 ( 7 y + 2 ) = 5 ( 6 y - 5 ) On further solving, ⇒ 77 y + 22 = 30 y - 25 (Removing brackets) ⇒ 77 y - 30 y = - 25 - 22 (Transposing 30 y to LHS and to RHS ) 47 y = - 47 ⇒ y = - 47 47 (Transposing 47 to RHS ) y = - 1 ∴ The solution of the given equation is y = - 1 .