Chapter 11: Algebra

(a) An equation with variable x

(b) An inequality equation

(c) No, it’s a numerical equation

(d) No, it’s a numerical equation

(e) An equation with variable x

(f) An equation with variable x

(g) An inequality equation

(h) An equation with variable n

(i) No, it’s a numerical equation

(j) An equation with variable p

(k) An equation with variable y

(l) An inequality equation

(m) An inequality equation

(n) No, it’s a numerical equation

(o) An equation with variable x

(a) 10y = 80

y = 10 is not a solution for this equation because if y = 10,

10y = 10 × 10

= 100 and not 80

(b) 10y = 80

y = 8 is a solution for this equation because if y = 8,

10y = 10 × 8

= 80

∴ Equation satisfied

(c) 10y = 80

y = 5 is not a solution for this equation because if y = 5,

10y = 10 × 5

= 50 and not 80

(d) 4l = 20

l = 20 is not a solution for this equation because if l = 20,

4l = 4 × 20

= 80 and not 20

(e) 4l = 20

l = 80 is not a solution for this equation because if l = 80,

4l = 4 × 80

= 320 and 20

(f) 4l = 20

l = 5 is a solution for this eqaution because if l = 5,

4l = 4 × 5

= 20

∴ Equation satisfied

(g) b + 5 = 9

b = 5 is not a solution for this equation because if b = 5,

b + 5 = 5 + 5

= 10 and not 9

(h) b + 5 = 9

b = 9 is not a solution for this equation because if b = 9,

b + 5 = 9 + 5

= 14 and not 9

(i) b + 5 = 9

b = 4 is a solution for this equation because if b = 4,

b + 5 = 4 + 5

= 9

∴ Equation satisfied

(j) h – 8 = 5

h = 13 is a solution for this equation because if h = 13,

h – 8 = 13 – 8

= 5

∴ Equation satisfied

(k) h – 8 = 5

h = 8 is not a solution for this equation because if h = 8,

h – 8 = 8 – 8

= 0 and not 5

(l) h – 8 = 5

h = 0 is not a solution for this equation because if h = 0,

h – 8 = 0 – 8

= – 8 and not 5

(m) p + 3 = 1

p = 3 is not a solution for this equation because if p = 3,

p + 3 = 3 + 3

= 6 and not 1

(n) p + 3 = 1

p = 1 is not a solution for this equation because if p = 1,

p + 3 = 1 + 3

= 4 and not 1

(o) p + 3 = 1

p = 0 is not a solution for this equation because if p = 0,

p + 3 = 0 + 3

= 3 and not 1

(p) p + 3 = 1

p = -1 is not a solution for this equation because if p = – 1,

p + 3 = -1 + 3

= 2 and not 1

(q) p + 3 = 1

p = -2 is a solution for this equation because if p = -2,

p + 3 = -2 + 3

= 1

∴ Equation satisfied

(a) 5m = 60

m = 12 is a solution for this equation because for m = 12,

5m = 5 × 12

= 60

∴ Equation satisfied

m = 10 is not a solution for this equation because for m = 10,

5m = 5 × 10

= 50 and not 60

m = 5 is not a solution for this equation because for m = 5,

5m = 5 × 5

= 25 and not 60

m = 15 is not a solution for this equation because for m = 15,

5m = 5 × 15

= 75 and not 60

(b) n + 12 = 20

n = 8 is a solution for this equation because for n = 8,

n + 12 = 8 + 12

= 20

∴ Equation satisfied

n = 12 is not a solution for this equation because for n = 12,

n + 12 = 12 + 12

= 24 and not 20

n = 20 is not a solution for this equation because for n = 20,

n + 12 = 20 + 12

= 32 and not 20

n = 0 is not a solution for this equation because for n = 0,

n + 12 = 0 + 12

= 12 and not 20

(c) p – 5 = 5

p = 10 is a solution for this equation because for p = 10,

p – 5 = 10 – 5

= 5

∴ Equation satisfied

p = 0 is not a solution for this equation because for p = 0,

p – 5 = 0 – 5

= -5 and not 5

p = 5 is not a solution for this equation because for p = 5,

p – 5 = 5 – 5

= 0 and not 5

p = -5 is not a solution for this equation because for p = -5,

p – 5 = -5 – 5

= – 10 and not 5

(d) q / 2 = 7

q = 14 is a solution for this equation because for q = 14,

q / 2 = 14 / 2

= 7

∴ Equation satisfied

q = 7 is not a solution for this equation because for q = 7,

q / 2 = 7 / 2 and not 7

q = 2 is not a solution for this equation because for q = 2,

q / 2 = 2 / 2

= 1 and not 7

q = 10 is not a solution for this equation because for q = 10,

q / 2 = 10 / 2

= 5 and not 7

(e) r – 4 = 0

r = 4 is a solution for this equation because for r = 4,

r – 4 = 4 – 4

= 0

∴ Equation satisfied

r = -4 is not a solution for this equation because for r = – 4,

r – 4 = – 4 – 4

= -8 and not 0

r = 8 is not a solution for this equation because for r = 8,

r – 4 = 8 – 4

= 4 and not 0

r = 0 is not a solution for this equation because for r = 0,

r – 4 = 0 – 4

= – 4 and not 0

(f) x + 4 = 2

x = -2 is a solution for this equation because for x = -2,

x + 4 = – 2 + 4

= 2

∴ Equation satisfied

x = 0 is not solution for this equation because for x = 0,

x + 4 = 0 + 4

= 4 and not 2

x = 2 is not a solution for this equation because for x = 2,

x + 4 = 2 + 4

= 6 and not 2

x = 4 is not a solution for this equation because for x = 4,

x + 4 = 4 + 4

= 8 and not 2

(a) For m + 10, the table is represented as below

Now, by inspection we may conclude that m = 6 is the solution of the above equation since, for m = 6,

m + 10 = 6 + 10 = 16

(b) For 5t, the table is represented as below

Now, by inspection we may conclude that t = 7 is the solution of the above equation since, for t = 7,

5t = 5 × 7 = 35

(c) For z / 3, the table is represented as below

z	z / 3
8	8 / 3 =
9	9 / 3 = 3
10	10 / 3 =
11	11 / 3 =
12	12 / 3 = 4
13	13 / 3 =
14	14 / 3 =
15	15 / 3 = 5
16	16 / 3 =

Now, by inspection we may conclude that z = 12 is the solution of the above equation since for z = 12,

z / 3 = 12 / 3 = 4

(d) For m – 7, the table is represented as below

Now, by inspection we may conclude that m = 10 is the solution of the above equation since, for m = 10,

m – 7 = 10 – 7 = 3

(i) There are 4 corners in a square.

Thrice the number of corners in the square = 3 × 4 = 12

When 12 is added to the number it becomes 34

So, the number will be the difference of 34 and 12

34 – 12 = 22

(ii) The result was 23 when the old number was up counted on Sunday

The result was 22 when the old number was up counted on Saturday

The result was 21 when the old number was up counted on Friday

The result was 20 when the old number was up counted on Thursday

The result was 19 when the old number was up counted on Wednesday

The result was 18 when the old number was up counted on Tuesday

The result was 17 when the old number was up counted on Monday

`Hence, the number taken at starting was 17 – 1 = 16

(iii) There are 11 players in a cricket team

If 6 is subtracted from a required number it will be 11

11 + 6 = 17

Hence, the number is 17

(iv) The required number is such that if it is subtracted from 22 the result is the number itself.

The number is 11 because if it is subtracted from 22 the result will be 11 only.

Disclaimer: 

Dropped Topics – 11.6 Use of variables in common rules, 11.7 Expressions with variables, 11.8 Using expressions practically, 11.9 What is an equation?, 11.10 Solution of an equation.

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