Question

Determine a solução real de cada uma das equações:

a) t\2 - 2\3 = 5t\6

b) y\4 + 1 = 7 - y\2

c) x+1\3 - x-1\6= 5\2 + x

d) 2(x-1)\3 - 3(x+1)\2= -(x+2)\6

Answer 1

$A)~~ \dfrac{t}{2} - \dfrac{2}{3} = \dfrac{5t}{6} \to~~mmc=6\\\\ 3t-4=5t\to\\\\ 3t-5t=4\to\\\\-2t=4~(-1)\to\\\\ 2t=-4\to\\\\ t=- \frac{4}{2} \to \\\\ \large\boxed{t=-2}$





$B)~~ \dfrac{y}{4} +1=7- \dfrac{y}{2} \to~~ mmc=4\\\\ y+4=28-2y\to\\\\ y+2y=28-4\to\\\\ 3y=24\to\\\\ y= \dfrac{24}{3} \to\\\\ \large\boxed{y=8}$





$C)~~ \dfrac{x+1}{3} - \dfrac{x-1}{6} = \dfrac{5}{2} +x\to~~mmc= 6\\\\ 2x+2-(x-1)=15+6x\to\\\\ 2x+2-x+1=15+6x\to\\\\ 2x-x-6x=15-2-1\to\\\\ -5x=12~(-1)\to\\\\5x=-12\to\\\\ \large\boxed{x=- \frac{12}{5} }$





$D)~~\dfrac{2(x-1)}{3} - \dfrac{3(x+1)}{2} =-\dfrac{(x+2)}{6} \to\\\\ \dfrac{2x-2}{3} - \dfrac{3x+3}{2} =\dfrac{-x-2}{6} \to ~~mmc=6\\\\ 4x-4-(9x+9)=-x-2\to\\\\ 4x-4-9x-9=-x-2\to\\\\ 4x-9x+x=-2+4+9\to\\\\ -4x=11\to\\\\ \boxed{x=- \frac{11}{4} }$