Question

Calculeaza (2x-3)/8 - (3x-2)/4 = (x+1)/2 si (x+3)/2 + (x-2)/4 = 5/6​

Answer 1

uite aici, sper ca am scris bine operatia

Answer 2

$\frac{2x-3}{8} -\frac{3x-2}{4} =\frac{x+1}{2}\,|\cdot8$

$8(\frac{2x-3}{8} -\frac{3x-2}{4} )=8\cdot\frac{x+1}{2}$

$\frac{8(2x-3)}{8} ^{(8}-\frac{8(3x-2)}{4} ^{(4}=\frac{8(x+1)}{2} ^{(2}$

$2x-3-2(3x-2)=4(x+1)$

$2x-3-6x+4=4x+4$

$2x-3-6x+4-4=4x$

$2x-3-6x=4x$

$2x-6x-3=4x$

$-4x-3=4x\implies -4x=4x+3$

$\implies -4x-4x=3\implies-8x=3\implies x=-\frac{3}{8}$

______________________

$\frac{x+3}{2} +\frac{x-2}{4} =\frac{5}{6} \,|\cdot12$

$12(\frac{x+3}{2} +\frac{x-2}{4} )=12\cdot\frac{5}{6}$

$\frac{12(x+3)}{2}^{(2} +\frac{12(x-2)}{4}^{(4} =\frac{12\cdot5}{6} ^{(6}$

$6(x+3)+3(x-2)=2\cdot5$

$6x+18+3x-6=10$

$9x+18-6=10$

$9x+12=10 \,|-12 \implies 9x=-2\implies x=-\frac{2}{9}$