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2cm And, if
: a :: 6 :c; then will =ab, or 2cx= 3
3ab 3ab ; or, by division, x=
43 Also, if 12
4:1; then 122
12 or 2x+x=12 ; and consequently x= -4.
1. Given 5x - 15=2x+6, to find the value of x. Here 52- 2x=6+15, or 3x=6+15321 ; and there
21 fore x
3 2. Given 40-62-16=120-14x, to find the value of c. Here 14x - 6x = 120-40+16'; or 8x = 136-40
96 96 ; and therefore x=3 =12
3. Given 3x2 - 10x=8x+x", to find the value of x.
Here 3.x—10=8+r, by dividing by w; or 3x -x=8 +-10=18, by transposition.
18 And consequently 2x=18, or x== =9.
2 4. Given 6ax3 12abr2 -3ax3 +6axa, to find the value
Here 2x - 46=2+2, by dividing by 3axo; or 2x-X =27-4b; and therefore c=46+2. 5. Given x2+2x+1=16, to find the value of
Here +1=4, by extracting the square root of each side.
And therefore, by transposition, x=4-1=3.
Here 5ax-2dx=c+3b; or (5a - 2d)x=c+36 ; and therefore, by division, a =
2 3 4
= 60; or
4 12x - 8x+6x=240 ; whence 10x=240, or x=24.
2 3 2 8. Given +
to find the value
2x Here 2-3+ =40-2+19; or 3x - 9+2x=120
3 3x+57 ; whence 3x + 2x+3x=120 + 57+9; that is 8.3=186, or x=231.
9. Giyen V5+5=7, to find the value of %.
Here v=7-5=2 ; whence, by squaring, 54, and 2x=12, or x=6.
2a2 10. Given : + v(az +xo)
to find the
✓(az +x2) value of x.
Here</a3+x2)+a? + x3 = 2a? ; or xv(as +x2)= a? – ,and x2(a2 +*2)=04 - 2ax3 +x4; whence ao 23 + x4=24 - 2a2x3 + x4, anda? x2 =a4- 202x; therefore3a222
a 4 a? =a4, or x2= ; and consequently
Ver 3a2 3 1 3 Fan
V3, the answer required. 3
1. Given 3x – 2+24=31, to find the value of x.
Ans. x=3 2. Given 4-9y=14-1ly, to find the value of Y.
Ans. y=5 3. Given x+18=3x - 5, to find the value of x.
Ans. x=113 4. Given x++-=11, to determine the value of x. 3=
+1=5x – 2, to find the value of x.
5. Given 2x
Ans. x= 3
7 6. Given +
to determine the value of x. 2 3 4
1 Ans. x=1
to find the value of x.
6 Ans. x=3
13 8. Given 2+73c=74-+-Ex, to find the value of x.
Ans. x=12 x2 9. Given uta= to find the value of x. uta
2 to find the value
10. Given vätvats=vlatz) of ton,
to find the value
36 Ans. x=
12. Given Va+*=Vb4+x", to find the value of x.
64 -0% Ans. 2=
13. Given va+x+va-=vax, to find the value
402 a2 +4
15. Given ata=vaz.txx(62+x2), to find the value
4a 16. Given iv x2 +3a%-ivX3 --3a2=Xva, to find the
9a3 value of x.
17. Given vatx+va-a=b, to find the value of x.
6 Ans. 2=
18. Given vata+va-=b, to find the value of x
Ans. x =
63 - 2a
19. Given vat vu=vax, to find the value of x.
Ans. x =
1 20. Given
=a, to determine the
21. Given as tax=a-vaz-ax, to find the value
V3. 22. Given vaz - x tavas -1=a? V1 -22, to find the value of x.
a2 +3 Given vata=c-vx+b, to find the value of x.
( -6 6
4bc 24. Given ✓ tváre ata
a? the value of x.
Of the resolution of simple equations, containing two
When there are two unknown quantities, and two independent simple equations involving them, they may be reduced to one, by any of the three following rules :
Observe which of the unknown quantities is the least involved, and find its value in each of the equations, by the methods already explained ; then let the two values, thus found, be put equal to each other, and there will arise a new equation with only one unknown quantity in it, the value of wbich may be found as before. (6)
(6) This rule depends upon the well known axiom, that things which are equal to the same thing, are equal to each other; and the two following methods are founded on principles which are equally simple and obvious,