Solve the following equation and check your result. 2 3 x = 3 8 x + 7 12

We have 2 3 x = 3 8 x + 7 12 ⇒ 2 3 x − 3 8 x = 7 12 ⇒ 2 × 8 − 3 × 3 24 x = 7 12 ⇒ 16 − 9 24 x = 7 12 ⇒ 7 24 x = 7 12 ⇒ x = 7 1 1 2 1 × 2 4 2 7 1 ⇒ x = 2 To check: Substitute the value of x in the given equation. LHS = 2 3 x = 2 3 × 2 = 4 3 RHS = 3 8 x + 7 12 = 3 8 × 2 + 7 12 = 6 8 + 7 12 = 6 × 3 + 7 × 2 24 = 3 2 4 2 4 3 = 4 3 ∴ LHS = RHS Hence, the value of x = 2 .

Solve the following equation and check your result. 3 x - 1 5 - x 7 = 3

We have 3 x - 1 5 - x 7 = 3 ⇒ 7 ( 3 x − 1 ) − 5 × x 35 = 3 ⇒ 21 x - 7 - 5 x 35 = 3 ⇒ 16 x − 7 35 = 3 ⇒ 16 x − 7 = 105 ⇒ 16 x = 105 + 7 ⇒ x = 1 1 2 7 1 6 1 = 7 To check: Substitute the value of x in the given equation. LHS = 3 x − 1 5 − x 7 = 21 - 1 5 - 7 7 = 20 5 - 1 = 3 RHS = 3 ∴ LHS = RHS Hence, the value of x = 7 .

Solve the following equation and check your result. y - 1 3 - y - 2 4 = 1

We have y − 1 3 − y − 2 4 = 1 ⇒ 4 ( y − 1 ) − 3 ( y − 2 ) 12 = 1 ⇒ 4 y − 4 − 3 y + 6 12 = 1 ⇒ y + 2 12 = 1 ⇒ y + 2 = 1 × 12 ⇒ y = 10 To check: Substitute the value of y in the given equation. LHS = y − 1 3 − y − 2 4 = 9 3 - 8 4 = 3 - 2 = 1 RHS = 1 ∴ LHS = RHS Hence, the value of y = 10 .

Solve the following equation and check your result. x - 2 4 + 1 3 = x - 2 x - 1 3

We have x − 2 4 + 1 3 = x − 2 x − 1 3 ⇒ x − 2 4 + 2 x − 1 3 − x = − 1 3 ( T ransposing - 2 x − 1 3 to LHS and 1 3 to RHS ) ⇒ 3 x − 6 + 8 x − 4 − 12 x 12 = − 1 3 ⇒ 11 x − 12 x − 10 = − 1 3 1 × 1 2 4 ⇒ − x = − 4 + 10 ⇒ x = − 6 To check: Substitute the value of x in the given equation. LHS = x − 2 4 + 1 3 = − 6 − 2 4 + 1 3 = - 8 4 + 1 3 = - 2 + 1 3 = - 5 3 RHS = x − 2 x − 1 3 = − 6 − 2 × ( − 6 ) − 1 3 = - 6 - - 13 3 = - 18 + 13 3 = - 5 3 ∴ LHS = RHS Hence, the value of x = - 6 .

Solve the following equation and check your result. 2 x - 1 3 - 6 x - 2 5 = 1 3

We have 2 x − 1 3 − 6 x − 2 5 = 1 3 ⇒ 5 ( 2 x − 1 ) − 3 ( 6 x − 2 ) 15 = 1 3 ⇒ 10 x − 5 − 18 x + 6 15 = 1 3 ⇒ − 8 x + 1 15 = 1 3 ⇒ − 8 x + 1 = 1 3 × 15 ⇒ − 8 x = 5 − 1 ⇒ − x = 4 8 ⇒ x = − 1 2 To check: Substitute the value of x in the following equation. LHS= 2 x − 1 3 − 6 x − 2 5 = - 1 - 1 3 - - 3 - 2 5 = - 2 3 - - 5 5 = - 2 3 + 1 = 1 3 RHS= 1 3 ∴ LHS = RHS Hence, the value x = - 1 2

Solve the following equation and check your result. y + 7 3 = 1 + 3 y - 2 5

We have y + 7 3 = 1 + 3 y - 2 5 ⇒ y + 7 3 = 5 × 1 + 3 y − 2 5 ⇒ 5 ( y + 7 ) = 3 ( 3 + 3 y ) ⇒ 5 y + 35 = 9 + 9 y ⇒ 9 y − 5 y = 35 − 9 ⇒ 4 y = 26 ⇒ y = 13 2 To check: Substitute the value of y in the given equation. LHS = y + 7 3 = 13 2 + 7 3 = 1 × 13 + 2 × 7 2 = 27 6 = 9 2 RHS = 1 + 3 y - 2 5 = 1+ 3 × 13 2 − 2 5 = 1 + 39 - 4 2 5 = 1 + 35 10 = 45 10 = 9 2 ∴ LHS = RHS Hence, the value of y = 13 2 .