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6.

8.0-8

= (2.6-2

6.62 –18x+12=27=3)*(32-6) }= 22–2

7. 899 +863 ard 12a2-24ab-3662 4 (2a3 +265)

4 (3a-6ab-96) 3a2-6ab-962) 12a +1263 (4a +86

1223-24a2b-36ab2

24a2b + 36ab2 +1263
24a2b-48ab2-7263

2162) 84ab2 +8463 Multiplying last

30–96 divisor by 4 4a +46) 12a-24nb-36bo (

12a + 12ab

- 36ab- 3662 -36ab--- 3662

8. 4a$y2-81278 and 2a”ya (2a-4y)

12ay +Gałys 2aạyo (6a®y +3a^y

2ay?

9. (

2+) and 25-4-2-3 (2-2 + ) = +2.23 + x2 Then w+ + 2003 + x)25-4-2-3 (2-3

25 +224 + 703

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24 + 2003

23 +22 203 +22

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10. 203 +"-9.1-9) 23 - 5.0 +2.2 +12 (1 23 + 2— 9x - 9

( -»–17 - 6x2 +112+21) 6x? +6.2.2-541-54

6.03 - 11x.-21x 11) 11x-33

1722 -33x-54 1-3) -6° +11x+21 (-6x-7

6 -6x2 + 18x

102x2—198x— 324 -7X+21

102.02–187x— 357 – 7x+21

11.
23 — 40? - 25x+28 ) (x2 + 3x— 4
and 2-14. +49 (x-7)(x-7)

12.
22 + 10m2 + 25x— 28 (x+7) (x2 + 3x +4)
and 2 +14. +49

=x +7 (x+7) (x+7) 13. 203-92? + 15x (x-2) (x2-7c+1)2 -2 & 2?–4 (2-2) (x+2)

=&--2

14. a’ + 40-5, a? + 7a

(a+5) (a-1) ) =a +4a-5 +10 and a-5

= (a +5) (a+2) =a + 7a-10 (a+5) (a-5) J =a?— 25

15. ai +1 and a3 + (a+1) (a?—a+1) ba' + ab +1

=a+1 (2+1) (a + ab-a+1) 16. a-3x+2, a'-a

(a-2) (a-1) 2 and a -4a+4

= (a-2) (a+1) =Q-2

(a-2) (a-2)

17. b+by-yo-y and b+by-ya-yo=(y+1) (b-y)

12 +by+32 +63 6+by+ya+ya=(y+1) (6+ya)

9+1)}

} }

=a+1

18. a'-a-2 (a+1) (a-2)

and 1+a3 (6+1) (a? +*+1) 19. 3a? + 4a-4 and (3a-2) (a+2)

3a +a-2 (32—2) (a+1)

}=a-
}

= 2a--2

SIMPLE EQUATIONS. 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 a+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 a+a=17.

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

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

4 4

same

1. @ +6=5x— 3x x+6=23

x=6

2. dxc=a

dx=ato

ato
à

3. x+c=24+c =24 4.

2x + 2=6
2x + x = 6

3x=6

a=2

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[blocks in formation]

-18=10x 48x— 3x—72=40x x=147

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10. 2x-1
2x

2+2
+ 6

12x 4x + 2=3x +42 3 2

X = 8 II.

36x +78 5x +42=

252 +210=360 +78 x=12

5 12. 4ax + 2b = 6cx + 8a 2ax 3cx = 4a 6

4x

2a-3c 13. 3x-3 3x-4_8_27+4a

272 - 27 – 36x + 8

6 3
48=192-108–16x 7x=63

x=9
14. 10x +5-6+2x=23 =2
15. 9x +20_12x— 36 3x

+

X = 8 12 5x—4 4 16. 1 2

2

18

14a +98 - 28a + 28= a+7 140-14 2a + 14

a=7

a-1

17.

3a
+ =x-13 70+ 15x=35x—455 =35
5 7

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+

19. 2 2C
+=+=1 6x + 3x + 2x=12

a=li
2.4.6
20. 7+7=12+62 X=5
21. 3x—3=9+x x=6
22. 5x +15=21—2 6x=6

x=1 23.

+*+ a=36 40€ + 3x + 2x=432 x=48

3 4.6 24. 20 20

+ =x+2 6x +4.0+3.0=12x + 24 x=24 23.4 25. 2a 2x- =12+2 10x— 2x=60+ 5.0 x=20

5 26. 2x 2 +

+10 6x + 4.0 - 3x= 3x + 60 x=15 3 2 2 27. 3x +3_* + 2

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=

6x+6=5x+10+30 x=34 5 28. 212_28

(x+4) 7x=224 x=32 2 3 29. 30, 60

+ L=14 70x=210 x=3

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

x=-1 31. 3x +8

X-8 2

=1
15

3
40=60 x=4

1. 5a +50=40+56
2. 16-11=7y +70
3. 24a +14=19a +49

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

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