**Simple Equations**

## Exercise 4.2

1). Give first the step you will use to separate the variable and then solve the equation:

(a) *x *– 1 = 0 (b) *x *+ 1 = 0

(c) *x *– 1 = 5 (d) *x *+ 6 = 2

(e) *y *– 4 = – 7 (f) *y *– 4 = 4

(g) *y *+ 4 = 4 (h) *y *+ 4 = – 4

Solution:

(a) *x *– 1 = 0

Adding 1 to both the sides

*x *– 1 + 1 = 0 + 1

*x *– 0 = 1

*x *= 1

(b) *x *+ 1 = 0

subtracting 1 to both the sides

*x *+ 1 – 1 = 0 – 1

*x *+ 0 = -1

*x *= -1

(c) *x *– 1 = 5

Adding 1 to both the sides

*x *– 1 + 1 = 5 + 1

*x *– 0 = 6

*x *= 6

(d) *x *+ 6 = 2

subtracting 6 from both the sides

*x *+ 6 – 6 = 2 – 6

*x *+ 0 = -4

*x *= -4

(e) *y *– 4 = – 7

Adding 4 to both the sides

*y *– 4 + 4 = -7 + 4

*y *– 0 = -3

*y *= -3

(f) *y *– 4 = 4

Adding 4 to both the sides

*y *– 4 + 4 = 4 + 4

*y *– 0 = 8

*y *= 8

(g) *y *+ 4 = 4

subtracting 4 from both the sides

*y *+ 4 – 4 = 4 – 4

*y *+ 0 = 0

*y *= 0

(h) *y *+ 4 = – 4

subtracting 4 from both the sides

*y *+ 4 – 4 = -4 – 4

*y *+ 0 = -8

*y *= -8

2). Give first the step you will use to separate the variable and then solve the equation:

(a) 3*l *= 42 (b)^{b}*/*_{2} = 6

(c) ^{p}*/*_{7} = 4 (d) 4*x *= 25

(e) 8*y *= 36 (f) ^{z}*/*_{3} = 5/4

(g) ^{a}*/*_{5} = 7/15 (h) 20*t *= – 10

Solution:

(a) 3*l *= 42 (b)^{b}*/*_{2 }= 6

(c) ^{p}*/*_{7} = 4 (d) 4*x *= 25

(e) 8*y *= 36 (f) *z/*_{3} = ^{5}/_{4}

(g) ^{a}*/*_{5} = 7/15 (h) 20*t *= – 10

3). Give the steps you will use to separate the variable and then solve the equation:

(a) 3*n *– 2 = 46 (b) 5*m *+ 7 = 17

(c) ^{20p}/_{3} = 40 (d) ^{3p} / _{10} = 6

Solution

(a) 3*n *– 2 = 46

Adding 2 to both the sides

3*n *– 2 + 2 = 46 + 2

3*n * = 48

Dividing both the sides by 3

^{3}* ^{n}* /

_{3}=

^{48}/

_{3}

*n* = 16

(b) 5*m *+ 7 = 17

Subtracting 7 from both the sides

5*m *+ 7 – 7 = 17 – 7

5*m *= 10

Dividing both the sides by 5

5*m */5 = 10/5

*m* = 2

(c) 20p/3 = 40

Multiplying 3 to both the sides

^{20}* ^{p}*/

_{3}X 3 = 40 X 3

20*p *= 120

Dividing both the sides by 20

^{20}* ^{p}* /

_{20}=

^{120}/

_{20}

*p* = 6

(d) ^{3p} / _{10} = 6

Multiplying 10 to both the sides

^{3}* ^{p}*/

_{10}X 10 = 6 X 10

3*p *= 60

Dividing both the sides by 20

^{3}* ^{p}* /

_{3}=

^{60}/

_{3}

*p* = 20

4). Solve the following equations:

(a) 10*p *= 100 (b) 10*p *+ 10 = 100

(c) ^{p}*/*_{4} = 5 (d) ^{–p} /_{3} = 5

(e) ^{3p} / _{4} = 6 (f) 3*s *= –9

(g) 3*s *+ 12 = 0 (h) 3*s *= 0

(i) 2*q *= 6 (j) 2*q *– 6 = 0

(k) 2*q *+ 6 = 0 (l) 2*q *+ 6 = 12

Solution

(a) 10*p *= 100

Dividing both the sides by 10

^{10p}/_{10} = ^{100}/_{10}

*p *= 10

(b) 10*p *+ 10 = 100

Subtracting 10 from both the sides

10*p *+ 10 – 10 = 100 – 10

10*p *= 90

Dividing both the sides by 10

^{10}* ^{p}*/

_{10}=

^{90}/

_{10}

*p* = 9

(c) ^{p}*/*_{4} = 5

Multiplying both the sides by 4

* ^{p}*/

_{4}X 4 = 5 X 4

*p *= 20

(d) ^{–p} /_{3} = 5

Multiplying both the sides by 3

^{–p} /_{3} X 3 = 5 X 3

–*p* = 15

*p* = -15

(e) ^{3p} / _{4} = 6

Multiplying both the sides by 4

^{3p} /_{4} X 4 = 6 X 4

3*p* = 24

Dividing both the sides by 3

^{3p}/_{3} = ^{24}/_{3}

3p = 8

(f) 3*s *= –9

Dividing both the sides by 3

^{3s} / _{3} = ^{-9}/_{3}

*s* = -3

(g) 3*s *+ 12 = 0

Subtracting 12 from both the sides

3*s *+ 12 – 12 = 0 – 12

3*s *= -12

Dividing both the sides by 3

3*s*/3 = -12/3

*s *= -4

(h) 3*s *= 0

Dividing both the sides by 3

^{3s}/_{3} = ^{0}/_{3}

*s* = 0

(i) 2*q *= 6

Dividing both the sides by 2

^{2q}/_{2} = ^{6}/_{2}

q = 3

(j) 2*q *– 6 = 0

Adding both the sides by 6

2q – 6 + 6 = 0 + 6

2q = 6

q = 3

(k) 2*q *+ 6 = 0

Subtracting 6 from both the sides

2*q* + 6 – 6 = 0 – 6

2*q* = -6

Dividing both the sides by 2

^{2q}/_{2} = ^{-6}/_{2}

*q* = -3

(l) 2*q *+ 6 = 12

Subtracting 6 from both the sides

2*q* + 6 – 6 = 12 – 6

2*q* = 6

Dividing both the sides by 2

^{2q}/_{2} = ^{6}/_{2}

*q* = 3

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