**Simple Equations**

## Exercise 4.3

1). Solve the following equations:

(a) 2* y* + ^{5}/_{2} = ^{37}/_{2} (b) 5*t *+ 28 = 10

(c) ^{a}*/*_{5} + 3 = 2 (d) ^{q}*/*_{4} + 7 = 5

(e) ^{5}/_{2} *x* = –5 (f) ^{5}/_{2} *x* = ^{2}^{5}/_{4}

(g) 7*m*+ ^{19}/_{2} =13 (h) 6*z *+ 10 = –2

(i) ^{3}* ^{ l}* /

_{2}=

^{2}/

_{3}(j)

^{2b}/

_{3}– 5 = 3

Solution

(a) 2* y* + ^{5}/_{2} = ^{37}/_{2}

(b) 5*t *+ 28 = 10

(c) ^{a}*/*_{5} + 3 = 2

(d) ^{q}*/*_{4} + 7 = 5

(e) ^{5}/_{2} *x* = –5

(f) ^{5}/_{2} *x* = ^{2}^{5}/_{4}

(g) 7*m*+ ^{19}/_{2} =13

(h) 6*z *+ 10 = –2

(i) ^{3}* ^{ l}* /

_{2}=

^{2}/

_{3}

(j) ^{2b}/_{3} – 5 = 3

2). Solve the following equations:

(a) 2(*x *+ 4) = 12 (b) 3(*n *– 5) = 21

(c) 3(*n *– 5) = – 21 (d) – 4(2 + *x*) = 8

(e) 4(2 – *x*) = 8

Solution

(a) 2(*x *+ 4) = 12

By removing the bracket we get

2*x *+ 8 = 12

Subtracting 8 from both the sides

2*x *+ 8 – 8 = 12 – 8

2*x *= 4

Dividing both the sides by 2

^{2}* ^{x}*/

_{2}=

^{4}/

_{2}

*x * = 2

(b) 3(*n *– 5) = 21

By removing the bracket we get

3*n *– 15 = 21

Adding 15 to both the sides

3*n *– 15 + 15 = 21 + 15

3*n *= 36

Dividing both the sides by 3

^{3}* ^{n}*/

_{3}=

^{36}/

_{3}

*n * = 12

(c) 3(*n *– 5) = – 21

By removing the bracket we get

3*n *– 15 = -21

Adding 15 to both the sides

3*n *– 15 + 15 = -21 + 15

3*n *= -6

Dividing both the sides by 3

^{3}* ^{n}*/

_{3}=

^{-6}/

_{3}

*n * = -2

(d) – 4(2 + *x*) = 8

By removing the bracket we get

-8 – 4*x* = 8

Adding 8 to both the sides

-8 – 4*x *+ 8 = 8 + 8

– 4*x* = 16

Dividing both the sides by 4

^{-4}* ^{x}*/

_{4}=

^{16}/

_{4}

–*x * = 4

*x * = -4

(e) 4(2 – *x*) = 8

By removing the bracket we get

8 – 4*x* = 8

Subtracting 8 from both the sides

8 – 4*x *– 8 = 8 – 8

– 4*x* = 0

Dividing both the sides by 4

^{-4}* ^{x}*/

_{4}=

^{0}/

_{4}

–*x * = 0

*x * = 0

3). Solve the following equations:

(a) 4 = 5(*p *– 2) (b) – 4 = 5(*p *– 2)

(c) 16 = 4 + 3(*t *+ 2) (d) 4 + 5(*p *– 1) =34

(e) 0 = 16 + 4(*m *– 6)

Solution:

(a) 4 = 5(*p *– 2)

Removing brackets we have

4 = 5*p* – 10

Transposing -10 to LHS

4 +10 = 5*p*

14 = 5*p*

Transposing 5 to LHS

^{14}/_{5} = *p*

*p* =^{14}/_{5}

(b) – 4 = 5(*p *– 2)

Removing brackets we have

-4 = 5*p* – 10

Transposing -10 to LHS

-4 +10 = 5*p*

6 = 5*p*

Transposing 5 to LHS

^{6}/_{5} = *p*

*p* =^{6}/_{5}

(c) 16 = 4 + 3(*t *+ 2)

Removing brackets we have

16 = 4 + 3*t* + 6

16 = 10 + 3*t*

Transposing 10 to LHS

16 -10 = 3*t*

6 = 3*t*

Transposing 3 to LHS

^{6}/_{3} = *t*

2* = t *

*t* =2

(d) 4 + 5(*p *– 1) =34

Removing brackets we have

4 + 5*p* – 5 = 34

5*p* – 1 = 34

Transposing -1 to RHS

5*p* = 34 + 1

5*p* = 35

Transposing 5 to RHS

*p* =^{35}/_{5}

*p* = 7

(e) 0 = 16 + 4(*m *– 6)

Removing brackets we have

0 = 16 + 4*m* – 24

0 = 4*m* – 8

Transposing -8 to LHS

0 + 8 = 4*m*

8 = 4*m*

Transposing 4 to LHS

^{8}/_{4} = *m*

2 = *m*

*m* = 2

4). (a) Construct 3 equations starting with *x *= 2

*x *= 2

(b) Construct 3 equations starting with *x *= – 2

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