Question

Rezolvati ecuatiile urmatoare, amplificandu-le eventual cu un multiplu comun al numitorilor tuturor termenilor din ecuatie:
(x-1)/2 - (3x-2)/4 = 2
(2x-1)/10 - x/4 = 1 - (3x+1)/8
2/3 - (x-1)/6 + (4-3x)/9 = (x-5)/2
2 * (2x-1)/3 - (x-5) = x/8 + (x+7)/6
-2/3 = (4x-1)/6 + 1/4 (x+1) -2



VA ROG AJUTATI.MA 99 DE PUNCTE

Answer 1

a)
(x-1)/2-(3x-2)/4=2
$\frac{2*(x-1)-(3x-2)}{4}=2 \\ \frac{-x}{4}=2 \\ -x=2*4 \\ -x=8 \\ x=8:-1 \\ x=-8$
b)
(2x-1)/10-x/4=1-(3x+1)/8
8x-4-10x=40-15x-5
-2x-4=-15x+35
13x=39
x=3
c)
[tex]\frac{2}{3}-\frac{x-1}{6}+\frac{4-3x}{9}=\frac{x-5}{2} \\ \frac{2*2-(x-1)}{6}=\frac{5-x}{6} \\ \frac{(5-x)*3+(4-3x)*2}{18}=\frac{23-9x}{18} \\ \frac{(23-9x)-[(x-5)*9]}{18}=\frac{68-18x}{18} \\ Cand -doua- fractii-sunt-egale-inseamna-ca-dau-0 \\ \frac{68-18x}{18}=0 \\ \\ \frac{-2*(9x-34)}{18} =0 \\ -2*(9x-34)=0*18 \\ -2*(9x-34)=0 \\ 9x-34=0 \\ 9x=0+34 \\ 9x=34 \\ x=34/9[/tex]
d)
2*(2x-1)/3 - (x-5) = x/8 + (x+7)/6
16(2x-1) - 24(x-5) =3x + 4(x+7)
32x-16 - 24x+120 =3x + 4x+28
8x+104=7x+28
x=-76
e)
-2/3 = (4x-1)/6 + 1/4 (x+1) -2
-8=8x-2+3x+3-24
-8=11x-23
11x=15
x=15/11
Sper ca te-am ajutat!
E bine?

Answer 2

$a).\displaystyle \frac{x-1}{2} - \frac{3x-2}{4} =2 \\ 2(x-1)-(3x-2)=2 \cdot 4 \\ 2x-2-3x+2=8 \\ 2x-3x=8+2-2 \\ -x=8 \\ x=-8 \\ b). \frac{2x-1}{10} - \frac{x}{4} =1- \frac{3x+1}{8} \\ 4(2x-1)-10x=40-5(3x+1) \\ 8x-4 -10x=40-15x-5 \\ 8x-10x+15x=40-5+4 \\ 13x=39 \\ x= \frac{39}{13} \\ x=3$
$\displaystyle c). \frac{2}{3} - \frac{x-1}{6} + \frac{4-3x}{9} = \frac{x-5}{2} \\ 6 \cdot 2-3(x-1)+2(4-3x)=9(x-5) \\ 12-3x+3+8-6x=9x-45 \\ -3x-6x-9x=-45-12-3-8 \\ -18x=-68 \\ x= \frac{68}{18} \Rightarrow x= \frac{34}{9}$
$\displaystyle d). \frac{2(2x-1)}{3} -(x-5)= \frac{x}{8} + \frac{x+7}{6} \\ \frac{4x-2}{3} -x+5= \frac{x}{8} + \frac{x+7}{6} \\ 8(4x-2)-24x+24 \cdot 5=3x+4(x+7) \\ 32x-16-24x+120=3x+4x+28 \\ 32x-24x-3x-4x=28+16-120 \\ x=-76$
$\displaystyle e).- \frac{2}{3} = \frac{4x-1}{6} + \frac{1}{4} (x+1)-2 \\ - \frac{2}{3} = \frac{4x-1}{6} + \frac{x+1}{4} -2 \\ -8=2(4x-1)+3(x+1)-12 \cdot 2 \\ -8=8x-2+3x+3-24 \\ -8x-3x=-2+3-24+8 \\ -11x=-15 \\ x= \frac{15}{11}$