Page 219 - Start Up Mathematics_6

Example 21: State which of the following are equations containing a variable. Identify the variable
involved in these equations.

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(a) 3x + 5 = 14 (b) 2y < 6 (c) > 2 (d) 3y – 2 = 0
3
3q
(e) 5 = (11 × 2) + p (f) 3 – 2y = 6y – 4 (g) < 6 (h) (5 – 2) + 13 = 8 × 2
2

Solution: (a) It is an equation with a variable x. (b) It is not an equation.
(c) It is not an equation. (d) It is an equation with a variable y.
(e) It is an equation with a variable p. (f) It is an equation with a variable y.
(g) It is not an equation. (h) It is an equation with no variable.

(5 – 2) + 13 = 8 × 2 is a numerical equation.

Example 22: Find whether the given values are solution of the equations or not. Write your answer
in the third column of the following table.

S. No. Equation Value of variable Equation satisfied (Yes/No)
(a) 5y = 30 y = 8
(b) 5y = 30 y = 6
(c) 5y = 30 y = 5
(d) 3m = 12 m = 4
(e) 3m = 12 m = 5
(f) 3m = 12 m = 10
(g) k + 3 = 1 k = 1

(h) k + 3 = 1 k = –1
(i) k + 3 = 1 k = –2
Solution: S. No. Equation Value of variable Equation satisfied (Yes/No)
(a) 5y = 30 y = 8 No

(b) 5y = 30 y = 6 Yes
(c) 5y = 30 y = 5 No
(d) 3m = 12 m = 4 Yes
(e) 3m = 12 m = 5 No
(f) 3m = 12 m = 10 No
(g) k + 3 = 1 k = 1 No
(h) k + 3 = 1 k = –1 No

(i) k + 3 = 1 k = –2 Yes
Example 23: Pick out the solution from the values given in the bracket next to each equation.
Also show that the other values do not satisfy the equation.
p
(a) 4x = 20 (0, 4, 5) (b) = 2 (8, 10, –10)
5
Solution: (a) In the given equation, 4x = 20, on putting
x = 0, LHS = 4x = 4 × 0 = 0 ≠ RHS
x = 4, LHS = 4x = 4 × 4 = 16 ≠ RHS

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