MATHEMATICS IN EVERYDAY LIFE–8
MATHEMATICS IN EVERYDAY LIFE?8
Chapter 8 : Linear Equations in One Variable
ANSWER KEYS
EXERCISE 8.1
1. x ? 3 = 8
x =8 + 3
(By transposing ? 3)
x = 11
2. x + 7 = 15
x = 15 ? 7
(By transposing 7)
x=8
3. 5x = 20 Dividing both sides by 5, we get
5x 5
=
20 5
x=4
4. 2x + 6 = 10
2x = 10 ? 6
2x = 4
(By transposing 6)
2x 4
2 =2
(On dividing both sides by 2)
x=2
5. 7x ? 5 = 16
7x = 16 + 5
7x = 21
(By transposing ? 5)
7x 21 7 = 7 (On dividing both sides by 7)
x=3
3x 6. 2 = 18
Multiplying both sides by 2, we get
3x 2 ? 2 = 18 ? 2
3x = 36
3x 36
3 = 3 (On dividing both sides by 3)
x = 12
Mathematics In Everyday Life-8
x 7. 5 = 7
x ?5=7?5 5 (On multiplying both sides by 5)
x = 35
8.
4 7
+ x =
20 7
x =
20 7
?
4 7
(By transposing
4 7)
20 4
x= 7
x = 16
7
9. 7 = 2x ? 5
or 2x ? 5 = 7
2x = 7 + 5
2x = 12
(By transposing ? 5)
2x = 12 (On dividing both sides by 2)
22
x=6
10. 1.6x + 2 = 5.2
1.6x = 5.2 ? 2
1.6x = 3.2
(By transposing 2)
1.6x 3.2 1.6 = 1.6 (On dividing both sides by 1.6)
x=2
11. 13 + 2a = 39
2a = 39 ? 13
2a = 26
(By transposing 13)
2a = 26
(On dividing both sides by 2)
22
a = 13
1
12. 16a ? 4 = 28
16a = 28 + 4
16a = 32
(By transposing ? 4)
16a 32 16 = 16 (On dividing both sides by 16)
a=2
EXERCISE 8.2
1. 2x ? 5 = 3x + 5
Transposing variables on L.H.S. and constant terms on R.H.S., we get
2x ? 3x = 5 + 5
? x = 10
x = 10 (On multiplying both sides by ? 1)
2. 9x + 15 = 20 ? x
Transposing variables on L.H.S. and constant terms on R.H.S., we get
9x + x = 20 ? 15
10x = 5
10x 10
=
5 10
(On dividing both sides by 10)
x= 1
2
3
4
3. 2m ? 5 = m + 5
Transposing variables on L.H.S. and constant terms on R.H.S., we get
2m ? m =
4 5
+
3 5
m=7
5
4. 3m + 4 = 8m + 24
Transposing variables on L.H.S. and constant terms on R.H.S., we get
3m ? 8m = 24 ? 4
? 5m = 20
5m 20 5 =5
(On dividing both sides by 5)
? m =4
m = 4 (On multiplying both sides by ? 1)
m 5. 2 + 6 = m ? 8
Transposing variables on L.H.S. and constant terms on R.H.S., we get
2
m 2 ?m= ?8?6
m = ? 14
2
(?
2)
m 2
=
(? 14) ? (?
2)
(On multiplying both sides by ? 2)
m = 28
6. 7 ? x = 4 ? x 3
Transposing variables on L.H.S. and constant terms on R.H.S., we get
? x +x=4?7 3
x 3x = ? 3 3
2x 3
=? 3
2x 3 ? 3 = ? 3 ? 3 (On multiplying both sides by 3)
2x = ? 9
2x = 9 (On dividing both sides by 2)
22
x= 9
2
72 7. 3t + 5 = 5 + 5t
or 2 + 5t = 3t + 7
5
5
Transposing variables on L.H.S. and constant terms on R.H.S., we get
72 5t ? 3t = 5 ? 5
2t
=
5 5
2t = 1
2t 2
=
1 2
(On dividing both sides by 2)
t= 1
2
8. 3.5x ? 9 = 2.4x + 13
Transposing variables on L.H.S. and constant terms on R.H.S., we get
Answer Keys
3.5x ? 2.4x = 13 + 9
1.1x = 22
1.1x 22
1.1 = 1.1 (On dividing both sides by 1.1)
x = 20
4
5
9. 11x ? 3 = 2x + 3
Transposing variables on L.H.S. and constant terms on R.H.S., we get
54 11x ? 2x = 3 + 3
9
9x = 3
9x = 3
9x 9
=
3 9
(On dividing both sides by 9)
x= 1
3
10.
12x ? 2 7
13 = 14 ? 5x
Transposing variables on L.H.S. and constant terms on R.H.S., we get
13 2 12x + 5x = 14 + 7
17x = 17
14
17x 17
=
17 14 17
(On dividing both sides by 17)
x= 1
14
EXERCISE 8.3
4x 1 1. 5x 2 = 1
4x ? 1 = 5x + 2
? 1 ? 2 = 5x ? 4x
?3=x
x=3
(By cross multiplication) (By transposing)
Verification: L.H.S. = 4( 3) 1 = 12 1 5( 3) 2 15 2
= 13 = 1 = R.H.S. 13
Mathematics In Everyday Life-8
2.
x 5 3 2x
=
5 3
3(3x + 5) = 5(3 ? 2x)
9x + 15 = 15 ? 10x
9x + 10x = 15 ? 15
19x = 0
0 x = 19 = 0
x=0
(By cross multiplication) (By transposing)
Verification: L.H.S. =
3(0) 5 3 2(0)
=
05 30
= 5 = R.H.S. 3
2x 3 9 3. 3x 2 = 7
7(2x + 3) = 9(3x + 2)
14x + 21 = 27x + 18
21 ? 18 = 27x ? 14x
13x = 3
3 = 13x
(By cross multiplication) (By transposing)
13x 13
=
3 13
(On dividing both sides by 13)
x= 3
13
Verification: L.H.S. =
2
3 13
3
=
6 3 13
3
3 13
2
9 13
2
6 39 45
=
13 9 26
=
13 35
13
13
= 45 = 9 = R.H.S. 35 7
4. (3x 4) 2x = ? 9
(2 5x) 7x
58
3x 4 2x 2 5x 7x
=?
9 58
x4 =? 9
2 12x
58
58(x + 4) = ?9(2 ? 12x)
(By cross multiplication)
58x + 232 = ? 18 + 108x
3
58x ? 108x = ? 18 ? 232
(By transposing)
? 50x = ? 250
50x = 250
50 50
(On dividing both sides by ?50)
x=5
Verification: L.H.S. = (3 5 4) 2 ? 5 (2 5 ? 5) 7 ? 5
= (15 4) 10 = 19 10 (2 25) 35 23 35
= 9 = ? 9 = R.H.S.
58
58
1
1
5. 2 (m ? 1) + 5 = 3 (2m + 1)
Multiplying both sides by 6, the L.C.M. of 2 and 3,
we get
6 ? 1 (m ? 1) + 6 ? 5 = 6 ? 1 (2m + 1)
2
3
3(m ? 1) + 30 = 2(2m + 1)
3m ? 3 + 30 = 4m + 2
? 3 + 30 ? 2 = 4m ? 3m
(By transposing)
25 = m
m = 25
Verification: L.H.S. = 1 (25 ? 1) + 5 = 1 ? 24 + 5
2
2
= 12 + 5 = 17
R.H.S. = 1 (2 ? 25 + 1) = 1 (50 + 1)
3
3
= 1 ? 51 = 17 3
L.H.S. = R.H.S.
6. 5x = ? 5 3x 4
5x = ? 5(3x + 4)
5x = ? 15x ? 20
5x + 15x = ? 20
20x = ? 20
(By cross multiplication) (By transposing)
20x = 20 (On dividing both sides by 20)
20 20
x=1
Verification: L.H.S. = 5 ? ( 1) = 5 3 ? ( 1) 4 3 4
= 5 = ? 5 = R.H.S. 1
4
2y 7. 3y 1 = ? 3
2y = ? 3(3y + 1)
2y = ? 9y ? 3
2y + 9y = ? 3
11y = ? 3
(By cross multiplication) (By transposing)
y = 3 (On dividing both sides by 11)
11
Verification: L.H.S. =
2
3 11
=
6 11
3
3 11
1
9 1 11
6
6
=
11 9 11
=
11 2
11
11
= 6 = ? 3 = R.H.S. 2
8.
1.2x 3 3.2x 6
=
9 8
8(1.2x + 3) = 9(3.2x + 6)
(By cross multiplication)
9.6x + 24 = 28.8x + 54
24 ? 54 = 28.8x ? 9.6x (By transposing)
? 30 = 19.2x
30
x = 19.2
(On dividing both sides by 19.2)
x = 300
192
x = 25
16
Verification: L.H.S. =
1.2
?
25 16
3
3.2
?
25 16
6
=
30 3 16 80 6 16
30 48 18
=
16 80 96
=
16 16
16
16
= 18 = 9 = R.H.S. 16 8
Answer Keys
9.
4y 8 5y 8
=
5 6
6(4y + 8) = 5(5y + 8)
24y + 48 = 25y + 40
48 ? 40 = 25y ? 24y
8 =y
(By cross multiplication) (By transposing)
y=8
Verification: L.H.S. = 4 ? 8 8 = 32 8 5 ? 8 8 40 8
xb xb 10. a b = a b
= 40 = 5 = R.H.S. 48 6
(x + b) (a + b) = (a ? b) (x ? b)
(By cross multiplication)
ax + bx + ab + b2 = ax ? ab ? bx + b2
ax + bx ? ax + bx = ? ab + b2 ? ab ? b2
(By transposing)
2bx = ? 2ab
2ab
x = 2b
(On dividing both sides by 2b)
x=a
Verification: L.H.S. = a b = (a b) = ? 1
ab
a b
R.H.S. = a b = (a b) = ? 1
ab
a b
11. 7x 4 = ? 4
x 2
3
3(7x + 4) = ? 4(x + 2)
21x + 12 = ? 4x ? 8
21x + 4x = ? 8 ? 12
25x = ? 20
(By cross multiplication) (By transposing)
x = ? 20 (On dividing both sides by 25)
25
x= 4
5
Verification: L.H.S. =
7
4 5
4
42
=
28 4 5 4 2
5
5
28 20 8
=
5 4 10
=
5 6
5
5
= 8 = 4 = R.H.S.
6
3
Mathematics In Everyday Life-8
12.
17(2 x) 5(x 12) 1 7x 7x 1
= 8
34 17x 5x 60 1 7x 7x 1
=8
34 17x 5x 60
1 7x 1 7x
=8
34 17x (5x 60) = 8 (1 7x)
34 17x 5x 60
(1 7x)
=8
22x 26 = 8
1 7x
? 22x ? 26 = 8(1 ? 7x)
(By cross multiplication)
? 22x ? 26 = 8 ? 56x
? 22x + 56x = 8 + 26
(By transposing)
34x = 34
x=1
(On dividing both sides by 34)
Verification: L.H.S. =
17(2 1) 5(1 12) 17?1 7?11
= 17 ? 1 5 13 = 17 65 17 71 6 6
4x 3 0.05 13. 10x 9 = 0.25
= 17 65 = 48 = 8 = R.H.S.
6
6
4x 3 5 1 10x 9 = 25 = 5
5(4x ? 3) = 1(10x ? 9) 20x ? 15 = 10x ? 9 20x ? 10x = ? 9 + 15
(By cross multiplication) (By transposing)
10x = 6
x= 6 =3
10 5
(On dividing both sides by 10)
x= 3
5
5
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