Solve the following equations and check the answers.
(a) 5z+1/3 = 7
(b) 5x/3 + 3 = x + 7
(a) (5z + 1)/3 = 7
⇒ (5z + 1)/3 × 3 = 7 × 3 (Multiplying both sides by 3)
⇒ 5z + 1 = 21
⇒ 5z = 21 − 1 (Transposing 1 to RHS)
⇒ 5z = 20
⇒ z = 20/5 (Dividing both sides by 5)
⇒ z = 4
Check: Put z = 4 in LHS
(5 × 4 + 1)/3 = 20 + 1/3 = 21/3 = 7 RHS as required.
(b) (5x/3) + 3 = x + 7 − 3
⇒ (5x/3) − x = 4 (Transposing 3 to RHS and x to LHS)
⇒ (5x − 3x)/3 = 4
⇒ 2x/3 = 4 (Multiplying both sides by 3)
⇒ 2x = 12
⇒ x = 12/2 (Dividing both sides by 2)
⇒ x = 6
Check: Put x = 6 in LHS
(5 × 6)/3 + 3 = 10 + 3 = 13
Put x = 6 in RHS
x + 7 = 13
LHS = RHS
Hence verified.