Given below are some equations and the values of the variables. Are these values the solutions to those equations? No. Equation Value of variable Solution(yes/No) 1 y - 3 = 11 y = 3 No 2 17 = n + 7 n = 10 3 30 = 5 x x = 6 4 m 2 = 14 m = 7

Given, No. Equation Value of variable Solution(yes/No) 1 y - 3 = 11 y = 3 No 2 17 = n + 7 n = 10 3 30 = 5 x x = 6 4 m 2 = 14 m = 7 The value of the variable which balances or satisfies the equation is called the ‘solution’ to the equation. We will verify if LHS = RHS, when the given value of the variable is substituted in the equation. ( 1 ) Putting y = 3 in the LHS of the equation, we get, LHS = y - 3 = 3 − 3 = 0 and RHS = 11 (given). Thus, LHS ≠ RHS which implies that y = 3 is not the solution of the equation y − 3 = 11 . Hence, No is given in the table. ( 2 ) Putting n = 10 in the RHS of the equation, we get, RHS = n + 7 = 10 + 7 = 17 and LHS = 17 (given). Thus, LHS = RHS which implies that n = 10 is the solution of equation 17 = n + 7 . ( 3 ) Putting x = 6 in the RHS of the equation, we get, RHS = 5 x = 5 × 6 = 30 and LHS = 30 (given). Thus, LHS = RHS which implies that x = 6 is the solution of the equation 30 = 5 x . ( 4 ) Putting m = 7 in the LHS of the equation, we get, LHS = m 2 = 7 2 and RHS = 14 (given). Thus, LHS ≠ RHS which implies that m = 7 is not the solution of the equation m 2 = 14 . Thus, the completed table is as follows: No. Equation Value of variable Solution(yes/No) 1 y - 3 = 11 y = 3 No 2 17 = n + 7 n = 10 Yes 3 30 = 5 x x = 6 Yes 4 m 2 = 14 m = 7 No

Solve the equation: P 4 = 9 .

Given, P 4 = 9 If the same operation is carried out on both sides of an equation every time, the equation remains balanced. P 4 = 9 Here, variable is divided by 4 . So, multiplying by 4 on both sides, we get, ⇒ P 4 × 4 = 9 × 4 ⇒ P 4 × 4 1 = 36 ⇒ P = 36 Thus, the solution of the given equation is P = 36 .