Solve the following linear equation. 5 x - 4 8 - x - 2 5 = x + 6 4

From the given, 5 x - 4 8 - x - 2 5 = x + 6 4 5 x - 4 8 - x - 2 5 - x + 6 4 = 0 ( Transposing x + 4 2 on L.H.S ) L.C.M of 8 , 5 and 4 is 40 . ⟹ 5 5 x - 4 - 8 x - 3 - 10 x + 4 40 = 0 ⟹ 5 × 5 x - 5 × 4 - 8 × x + - 8 × - 3 - 10 × x + - 10 × 4 40 = 0 ⟹ 25 x - 20 - 8 x + 24 - 10 x - 40 40 = 0 ⟹ 25 x - 8 x - 10 x - 20 + 24 - 40 40 = 0 ⟹ 7 x - 36 40 = 0 ⟹ 7 x - 36 40 × 40 = 0 × 40 ( Multiplying both sides 40 ) ⟹ 7 x - 36 = 0 ⟹ 7 x = 36 ( Transposing - 36 on R.H.S ) ⟹ x = 36 7 ( Transposing 7 on R.H.S) Hence, the required answer is as shown above.

Solve the following linear equation. y - 2 y - 3 y - 2 7 = 4 y - 3 3 - 3

From the given, y - 2 y - 3 y - 2 7 = 4 y - 3 3 - 3 ⇒ y - 2 y - 3 y - 2 7 = 4 y - 3 - 9 3 ⇒ y - 2 y - 3 y - 2 7 = 4 y - 12 3 ⇒ y - 2 y - 3 y - 2 7 - 4 y - 12 3 = 0 ( Transposing 4 y - 12 3 on L.H.S ) ⇒ y - 14 y - 3 y - 2 7 - 4 y - 12 3 = 0 ⇒ y - 11 y - 2 7 - 4 y - 12 3 = 0 ⇒ 21 y 21 - 3 11 y - 2 21 - 7 4 y - 12 21 = 0 ⇒ 21 y - 3 11 y - 2 - 7 4 y - 12 21 = 0 ⇒ 21 y - 33 y + 6 - 28 y + 84 21 = 0 ⇒ 21 y - 33 y - 28 y + 6 + 84 21 = 0 ⇒ 21 y - 61 y + 90 21 = 0 ⇒ - 40 y + 90 21 = 0 ⇒ - 40 y + 90 21 × 21 = 0 × 21 ( Multiplying both side on 21 ) ⇒ - 40 y + 90 = 0 ⇒ - 40 y = - 90 ( Transposing 90 on R.H.S ) ⇒ y = - 90 - 40 ( Transposing - 40 on R.H.S ) ∴ y = 9 4 Hence, the required answer is obtained.

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

From the given, 2 4 5 x - 1 - 2 x - 1 - x 4 = x + 1 4 ⇒ 2 4 5 x - 1 - 2 x - 1 - x 4 = 4 x + 1 4 ⇒ 2 4 5 x - 1 - 2 x - 1 - x 4 - 4 x + 1 4 = 0 ( Transposing 4 x + 1 4 on L.H.S ) ⇒ 10 x - 2 4 - 8 x - 1 - x 4 - 4 x + 1 4 = 0 ⇒ 10 x - 2 - 8 x - 1 - x - 4 x + 1 4 = 0 ⇒ 10 x - 2 - 8 x + 1 + x - 4 x - 1 4 = 0 ⇒ 10 x - 8 x - 4 x + x - 2 + 1 - 1 4 = 0 ⇒ 11 x - 12 x - 2 4 = 0 ⇒ - x - 2 4 = 0 ⇒ - x - 2 4 × 4 = 0 × 4 ( Multiplying 4 on both sides ) ⇒ - x - 2 = 0 ⇒ - x = 2 ∴ x = - 2 Hence, the required answer is obtained.

Solve the following linear equation. 8 x + 5 2 - x - x - 2 4 = 24

From the given, 8 x + 5 2 - x - x - 2 4 = 24 ⇒ 8 x + 5 2 - 4 x - x - 2 4 = 24 ⇒ 8 x + 5 2 - 4 x - x - 2 4 - 24 = 0 ( Transposing 24 on L.H.S ) ⇒ 4 8 x + 5 8 - 2 4 x - x - 2 8 - 8 24 8 = 0 ⇒ 32 x + 20 8 - 8 x - 2 x - 4 8 - 192 8 = 0 ⇒ 32 x + 20 - 8 x + 2 x + 4 - 192 8 = 0 ⇒ 32 x - 8 x + 2 x + 4 + 20 - 192 8 = 0 ⇒ 32 x - 6 x + 24 - 192 8 = 0 ⇒ 26 x - 168 8 = 0 ⇒ 26 x - 168 8 × 8 = 0 × 8 ( Multiplying 8 on both sides ) ⇒ 26 x - 168 = 0 ⇒ 26 x = 168 ⇒ 26 x 26 = 168 26 ( Dividing 26 on both sides ) ⇒ x = 168 26 = 84 13 ∴ x = 84 13 Hence, the required answer is obtained.