SOLUTION: solve each equation. PLEASE DO THESE FOR ME.. THANKS 1. x/3+x/2=10 2. y-3/5=y+1/7 3. x/2=2x-3 4. -1/4-2x/3 5. 1/x-1/6=4/3x^2 6. 2x-4/x-5=0

Question 196283: solve each equation. PLEASE DO THESE FOR ME.. THANKS
1. x/3+x/2=10
2. y-3/5=y+1/7
3. x/2=2x-3
4. -1/4-2x/3

5. 1/x-1/6=4/3x^2
6. 2x-4/x-5=0

Answer by anantha(86) (Show Source): You can put this solution on YOUR website!
sol:
1). x/3+x/2=10
take L.H.S part
x/3+x/2
the L.C.M OF 3 and 2 is 6
now multiplying through out the equation by 6
x/3*6+x/2*6=10*6
2x+3x=60
5x=60
dividing by 5 on both sides
5x/5=60/5
x=12
-------------------------------------------------------------------------------
3). x/2=2x-3
multiplying by 2 on both sides
x/2*2=2*(2x-3)
x=4x-6subtract x on both sides
x-x=4x-6-x
0=3x-6
adding 6 on both sides
0+6=3x-6+6
6=3x
dividing by 3 on both sides
6/3=3x/3
2=x
x=2
-------------------------------------------------------------------------------
5).
1/x-1/6=4/3x^2
take L.H.S part the lcm of 6 and x is 6x
6-x/6x
6-x/6x=4/3x^2
on cross multiplication
3x^2(6-x)=6x*4
18x^2-3x^3=24x
dividing through out by x
18x^2/x-3x^3/x=24x/x
18x-3x^2=24 take l.h.s terms on r.h.s side we can chabnge the signs
3x^2-18x+24=0
3x^2-12x-6x+24=0 (i.e;on multiplying 3 and 24 we get 72 the factors of 72 are 12 and 6 because on adding these two we get 18 and multiplying we get 72)
3x(x-4)-6(x-4)=0
(3x-6)(x-4)=0
3x-6=0
3x=6
x=6/3=2
x-4=0
x=4
x=4,2
-------------------------------------------------------------------------------
6).
2x-4/x-5=0
multiplying by x on both sides
2x*x-4/x*x-5*x=0*x
2x^2-4-5x=0
2x^2-5x-4=0
this is of the form ax^2+bx+c=0
here a=2,b=-5,c=-4
x=[-b+sqrt(b^2-4ac)]/2a, x=[-b-sqrt(b^2-4ac)]/2a
x=[-(-5)+sqrt((_5)^2-4*2*-4)]/2*2
x=[5+sqrt(25+32)]/4
x=[5+sqrt(57)]/4
x=[-sqrt(57)]/4

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