CPhill

OK......

3-x+2/3=3-2x/3+1/6     simplify

9/3 - x + 2/3 = 18/6 - 2x/3 + 1/6

11/3 - x = 17/6 - (2/3)x        multiply through by 6 to get rid of the fractions

22 - 6x = 17 - 4x                  add 6x to both sides

22 = 17 + 2x                        subtract 17 from both sides

5 = 2x                                  divide both sides by 2

5/2 = x

8x^2 - 6x + 1 = 0     factor, if we can

(4x - 1) (2x - 1) = 0   setting each factor to 0, we get    x = 1/4   and x = 1/2

I did this one a little differently...there is a "fudge factor" involved, but it's only a slight "fudge"

∫ x / √(3 - 4x^2) dx

let u = 3 - 4x^2    du  = -8x dx    du/-8 = x dx

So we have

-(1/8)∫u^(-1/2) du =

-(1/4)u^(1/2) + C =

-(1/4)(3 - 4x^2)^(1/2) + C

-

5^(x+3)=2^x    take the log of both sides

log5^(x+3)= log2^x    and we can write

(x+3) log 5 = xlog 2    simplify

xlog5 +3log5 = xlog2     rearrange

xlog5 - x log2  = -3log5    factorthe left side

x(log5 - log2) = -3log5      divide both sides by (log5 - log 2)

x = -3log5 / (log5 - log 2)  =   -5.2694123920980896

√3 / √2   =  √(3/2) = √1.5   which is irrational and can't be expressed as a fraction

6.26  =  6 + 26/100   =  6 + 13/50  = 313/50

Very well presented, Anonymous.....why don't you join up as a member???

7.3 / (8/9)  = x / 1    cross-multiply

7.3 = (8/9) x     multiply both sides by (9/8)

x = 8.2125 kg / bag

If the average of 8 numbers is 12, their sum must be 96....and if we increase each of them by 2, the new sum must be 16 more = 112

So 112 / 8 = 14     (and that's the new average......as we might have predicted!!!)