31.
a)
`x/2+25 = 3x-"12,5" " /"*2`
`x+50 = 6x-25 " /"-x`
`50 = 5x-25 " /"+25`
`5x = 75 " /":5`
`x = 15`

b)
`(2x)/3-cancel 12_3*x/cancel 4-(cancel 4 x)/cancel 12_3 = 3-2x`
`(2x)/3-3x-x/3 = 3-2x " /"*3`
`2x-9x-x = 9-6x`
`-8x = 9-6x " /"+8x`
`0 = 9+2x " /"-9`
`2x = -9 " /":2`
`x = -9/2`

c)
`(2x)/3-x/6 = x/4+1 " /"*12`
`8x-2x = 3x+12`
`6x = 3x+12 " /"-3x`
`3x = 12 " /":3`
`x = 4`

d)
`(2x)/3-x/6 = x/2+1 " /"*6`
`4x-x = 3x+6`
`3x = 3x+6 " /"-3x`
`0 = 6`
nincs megoldás

e)
`5*x/3-cancel 12_3*x/cancel 4-(cancel 4 x)/cancel 12_3 = 3-2x`
`(5x)/3-3x-x/3 = 3-2x " /"*3`
`5x-9x-x = 9-6x`
`-5x = 9-6x " /"+6x`
`x = 9`

f)
`(4x)/3-1/cancel 15_5*cancel 3 x+(7x)/20 = x+2`
`(4x)/3-x/5+(7x)/20 = x+2 " /"*60`
`80x-12x+21x = 60x+120`
`89x = 60x+120 " /"-60x`
`29x = 120 " /":29`
`x = 120/29`

g)
`3x-(1/2 x-5) = 5-(1/2 x-5) " /"+(1/2 x-5)`
`3x = 5 " /":3`
`x = 5/3`

h)
`3/4 x+1/8 x+1/2 x = x-2 " /"*8`
`6x+x+4x = 8x-16`
`11x = 8x-16 " /"-8x`
`3x = -16 " /":3`
`x = -16/3`

i)
`2x+2-(3+x/3) = x+1+(3+x/3)`
`2x+2-3-x/3 = x+1+3+x/3`
`2x-1-x/3 = x+4+x/3 " /"*3`
`6x-3-x = 3x+12+x`
`5x-3 = 4x+12 " /"-4x`
`x-3 = 12 " /"+3`
`x = 15`

j)
`x/2-(1-x/2) = 2x+3`
`x/2-1+x/2 = 2x+3`
`x-1 = 2x+3 " /"-x`
`-1 = x+3 " /"-3`
`x = -4`

32.
a)
`x/2+x/3-x/4 = 7 " /"*12`
`6x+4x-3x = 7*12`
`7x = 7*12 " /":7`
`x = 12`

b)
`x/5+(3x)/7-x/35 = 21 " /"*35`
`7x+15x-x = 21*35`
`21x = 21*35 " /":21`
`x = 35`

c)
`(3x)/2+x/6-(2x)/9 = 13 " /"*18`
`27x+3x-4x = 13*18`
`26x = 13*18 " /":26`
`x = (cancel 13*18)/cancel 26_2 = cancel 18_9/cancel 2 = 9`

d)
`x+(2x)/3-(3x)/4 = 11 " /"*12`
`12x+8x-9x = 11*12`
`11x = 11*12 " /":11`
`x = 12`