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Show that the other values do not satisfy the equation.

(a) 5m = 60 (10, 5, 12, 15)

(b) n + 12 (12, 8, 20, 0)

(c) p – 5 = 5 (0, 10, 5 ,– 5)

(d) \(\frac{q}{2} \) = 7 (7, 2, 10, 14)

(e) r – 4 = 0 (4, -4, 8, 0)

(f) x + 4 = 2 (-2, 0, 2, 4)

Answer :

(a) 5m = 60 (10, 5 , 12, 15)
For m = 10, LHS = 5 x 10 = 50, RHS = 60
Here, LHS \(\neq \)RHS

\(\therefore \)m = 10 is not the solution of the equation

For m = 5, LHS = 5×5 = 25, RHS = 60

Here, LHS \(\neq \) RHS

\(\therefore \) m = 5 is not the solution of the equation

For m = 12, LHS = 5 x 12 = 60, RHS = 60

Here, LHS = RHS

\(\therefore \) m = 12 is the solution of the equation

For m = 15 LHS = 5 x 15 = 75, RHS = 60

Here, LHS \(\neq \) RHS

\(\therefore \) m = 15 is not the solution of the equation

(b) n + 12 = 20 (12, 8, 20, 0)

For n = 12, LHS = 12 + 12 = 24, RHS = 20

Here, LHS \(\neq \) RHS

\(\therefore \) n = 12 is not the solution of the equation

For n = 8, LHS = 8 + 12 = 20, RHS = 20

Here, LHS = RHS

\(\therefore \) n = 8 is the solution of the equation

For n = 20, LHS = 20 + 12 = 32, RHS = 20

Here, LHS \(\neq \) RHS

\(\therefore \) n = 20 is not the solution of the equation

For n = 0, LHS = 0 + 12 – 12, RHS = 20

Here, LHS \(\neq \) RHS

\(\therefore \) n= 0 is not the solution of the equation

(c) p – 5 = 5 (0, 10, 5, -5)

For p = 0, LHS = 0 – 5 = -5, RHS = 5

Here, LHS \(\neq \) RHS

\(\therefore \) p = 0 is not the solution of the equation

For p = 10, LHS = 10 – 5 = 5, RHS = 5

Here, LHS = RHS

\(\therefore \) p = 10 is the solution of the equation

For p = 5, LHS = 5-5-0, RHS = 5

Here LHS \(\neq \) RHS

\(\therefore \) p = 5 is not the solution of the equation

For p = 5, LHS = 5 – 5 = 0, RHS = 5

Here, LHS \(\neq \) RHS

\(\therefore \) p = -5 is not the solution of the equation

(d) q/2 = 7 (7, 2, 10, 14)

For q = 7, LHS = 7/2 , RHS = 7

Here LHS \(\neq \) RHS

\(\therefore \) q = 7 is not the solution of the equation

For q = 2, LHS = 2/2 = 1, RHS = 7

Here, LHS \(\neq \) RHS

\(\therefore \) q = 2 is not the solution of the equation

For q = 10, LHS = 10/2 = 5, RHS = 7

Here, LHS \(\neq \) RHS

For q = 14, LHS = 14/2 = 7, RHS = 7

Here, LHS = RHS

\(\therefore \) q = 14 is the solution of the equation

(e) r – 4 = 0 (4, -4, 8, 0)

For r = 4, LHS = 4 – 4 = 0, RHS = 0

Here, LHS = RHS

\(\therefore \) r = 4 is the solution of the equation

For r = -4, LHS = -4 – 4 = -8, RHS = 0

Here, LHS \(\neq \) RHS

\(\therefore \) r = -4 is not the solution of the equation

For r = 8, LHS = 8 – 4 = 4, RHS = 0

Here, LHS \(\neq \) RHS

For r = 8 is not the solution of the equation

For r = 0, LHS = 0 – 4 = – 4, RHS = 0

Here, LHS \(\neq \) RHS

\(\therefore \) r = 0 is not the solution of the equation

(f) x + 4 = 2 (-2, 0, 2, 4)

For x = -2, LHS = -2 + 4 = 2, RHS = 2

Here, LHS – RHS

\(\therefore \) x = -2 is the solution of the equation

For x = 0, LHS = 0 + 4 – 4, RHS = 2

Here, LHS \(\neq \) RHS

\(\therefore \) x = 0 is not the solution of the equation

For x = – 2, LHS = -2 + 4 – 6, RHS = 2

Here, LHS \(\neq \) RHS

\(\therefore \) x = 2 is not the solution of the equation

For r = 4, LHS = 4 + 4 = 8, RHS = 2

Here, LHS \(\neq \) RHS

\(\therefore \)x = 4 is not the solution of the equation

- Q.1 State which of the following are equations (with a variable). Give reason for your answer. Identify the variable from the equations with a variable. (a) 17 = x + 17 (b) (t – 7) > 5 (c) \(\frac{4}{2} \) = 2 (d) (7 × 3) – 19 = 8 (e) 5 × 4 – 8 = 2x (f) x – 2 = 0 (g) 2m < 30 (h) 2n + 1 = 11 (i) 7 = (11 × 5) – (12 × 4) (j) 7 = (11 × 2) + p (k) 20 = 5y (l) \(\frac{2q}{2} \)< 5 (m) z + 12 > 24 (n) 20 – (10 – 5) = 3 × 5 (o) 7 – x = 5
- Q.2 Complete the entries in the third column of the table.
- Q.4 (a)Complete the table and by inspection of the table find the solution to the equation m + 10 = 16. (b) Complete the table and by inspection of the table, find the solution to the equation 5t = 35 (c) Complete the table and find the solution of the equation z / 3 = 4 using the table. (d) Complete the table and find the solution to the equation m – 7 = 3.
- Q.5 Solve the following riddles, you may yourself construct such riddles. Who am I? (i) Go round a square Counting every corner Thrice and no more! Add the count to me To get exactly thirty four! (ii) For each day of the week Make an upcount from me If you make no mistake You will get twenty three! (iii) I am a special number Take away from me a six! A whole cricket team You will still be able to fix! (iv) Tell me who I am I shall give a pretty clue! You will get me back If you take me out of twenty two!

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