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Having explained the four simple rules in Algebra,
we will now proceed to Simple Equations in which
these
may

be worked out.
An Equation is an expression in Algebra consisting
of two portions united by the sign =, such that the
quantity on the one side is the same in numerical
value as the other, as x +b=7.

If this equation contain an unknown in the 1st
power, that is not the square, cube, &c., it is called
a Simple Equation, as æta=17.

As the two halves of the equality, united by
=, are equal, the equality will not be destroyed by
adding, subtracting, multiplying, or dividing, pro-
vided we do the

to both sides of the
equation. Thus if x + a = 7, then x + a + 3=7+3,
and x + 3 = 7–3, and 4 (v + a) = 4 x 7 or
at at 7 7

4 4

same

1.

x+6=5x— 3x
@ +6=2x

x=6

2. dx-c=a

dx=ato

ato
d

3. x+c=24+c a=24 4. 2x + =6

2x + x = 6

3x=6

2=2

20

2x + 2

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re + :

6.

+-+ =174 2.4

3.57 6

15x 5x + 3x +

=2610 4 4

7 2x+x=6

15x 3x=6 X=2

=2610

7
56x +15x=18270

71.x=18270
18270

=25741

71 5x +4_4x-9

3x-10x-8=82-18 2 3

3 3x 12 -18=10x 48x - 3x—72=40x x=143

4

7.

8.

9.

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10.

2+2

+6

12x

4x +2=3x +42

X = 8

x=12

II.

36x +78 5x +42=

252 +210=36x + 78

5 12. 4ax + 2b = 6cx + 8a

2ax 3cx = 4a 6 4x

b

20-30 13. 3x—3 32—4_8 27+4a

27x 27 – 36x + 8 6 3

18 48=192-108–16x 7x=63 x=9 14. 10.C +5-6+2x=23 =2 15. 9x + 20 12x-36 , 32

+

2 = 8 12

5x -4 4 16. 1 2

2

14a +98 - 28a + 28= -1 a+7 14a-14

2a +14 a=7

a

17.

'=x-13 7x + 15x=35x—455 =35

+ Bar

--=85 282–70—4x=2380 <=140

18.

x=1

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19. 20 2C
+-+ =6x + 3x + 2x=12

x=lji
2'4'6
20. 7+7=12+62 =5
21. 3x—3=9 +20

x=6 22. 5x+15=21- 6x=6 23. +-+ -36

46 + 3x + 2x=432 x=48 3'4' 6 24.

2C t+=x+2 6x + 4x + 3x=1226 + 24 x=24

2 3.4 25. 2x 2.c

=12+ 10x-2x=60+52 x=20

5 26.

2 at

+10 6x +4.2-32=3.c +60 =15 3 2 27. 3x +3_2+2 +3 6x+6=5x+10+30

x=34 5 28. 21x28

(2+4) 7x=224 2 3 29. 30 60

+ =14 70x=210 x=3

5x 30. 2+3—4+8=6 x= -1 31. 3x +8 2-8 2

=1

12x + 32-52+40-40+ 15 12 3

2x

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x=32

40=60 x=4

1. 5a +50=40+56
2. 167–11=7y+70
3. 24a +14=19a +49

Ans. a=6
Ans. y=9
Ans. a=7

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Problems producing Simple Equations :

I divide 240 shillings among a certain number of boys, of whom, if there had been five more, each would have received 10s. How many boys are there ?

Let a = : No. of boys.
x+5=No. of boys in supposed case

240
and =10s.
a +5

240=102 +50

10x=190:.x=19=No.of boys. 1. I divide 60 marbles among two boys, so that the one has four times as many as the other. How many has each ?

Let x=No. of one boy's share.

then 4x=other's.
And v+4w=60:.x=12 and 4x=48.

= 33

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2. Divide 33 yards of silk so that one part may be of the other.

x = greater part Then a

= lesser 2 + x

x = 23; yds.

of 2310 = 18 = 910 yds. 3. What is that number which when trebled and added to 17 makes 97 ?

number Then 3x+17 = 97

2 = 263 4. Two boys are within 7 years of each other, the one being as much above 17 as the other is below it. What are their ages ?

a = age of younger
Then x = 17-}

131 :: 131 +7 = 20 = the age of the elder. 5. If I had three times as many marbles as I have, and 17 more I should have 47, how many have I ?

a = number Then 3x+17 = 47

: 10 6. I am three times as old as my son; six years ago I was five times as old. What is my age ?

æ = son's age
3x = father's age
3x-6 = 5 (x-6)
2x = 24

father's age = 36 7. It takes 75 yards of carpet for a room the breadth of which is 16 feet. What is its length ?

x = length 16x = 225 feet

147 feet

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a = 12

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