Question

exercițiul 20 va rogggggggggggggg din tot sufletul meu pls pls pls

Answer 1

$\displaystyle 20a). \frac{x+5}{5} - \frac{x+3}{4} = \frac{3x}{10} - \frac{x+1}{4} \\ \\ 4(x+5)-5(x+3)=2 \cdot 3x-5(x+1) \\ \\ 4x+20-5x-15=6x-5x-5 \\ \\ 4x-5x-6x+5x=-5-20+15\\ \\ -2x=-10 \Rightarrow x= \frac{10}{2} \Rightarrow \boxed{x=5}$

$\displaystyle b). \frac{x}{5} + \frac{x+4}{10} = \frac{x-1}{6} - \frac{1}{5} (x+3)+ \frac{11}{30} \\ \\ 6x+3(x+4)=5(x-1)- 6(x+3)+11 \\ \\ 6x+3x+12=5x-5-6x-18+11 \\ \\ 6x+3x-5x+6x=-5-18+11-12 \\ \\ 10x=-24 \Rightarrow x=- \frac{24}{10} \Rightarrow \boxed{x=- \frac{12}{5}}$

$\displaystyle c). \frac{5x-6}{3} - \frac{1}{2} (4x-7)= \frac{21}{6} - \frac{1}{3} (4x-10) \\ \\ 2(5x-6)-3(4x-7)=21-2(4x-10) \\ \\ 10x-12-12x+21=21-8x+20 \\ \\ 10x-12x+8x=21+20+12-21 \\ \\ 6x=32 \Rightarrow x= \frac{32}{6} \Rightarrow \boxed{x= \frac{16}{3} }$

$\displaystyle d). \frac{2x-5}{4} + \frac{x-7}{3} = \frac{4x+11}{4} -7 \frac{1}{12} \\ \\ 3(2x-5)+4(x-7)=3(4x+11)- 85 \\ \\ 6x-15+4x-28=12x+33-85 \\ \\ 6x+4x-12x=33-85+15+28 \\ \\ -2x= -9 \Rightarrow \boxed{x= \frac{9}{2} }$

$\displaystyle e). \frac{2x-1}{3} - \frac{x-5}{2} = \frac{5x+8}{6} - \frac{2x-7}{2} \\ \\ 2(2x-1)-3(x-5)=5x+8-3(2x-7) \\ \\ 4x-2-3x+15=5x+8-6x+21 \\ \\ 4x-3x-5x+6x=8+21+2-15 \\ \\ 2x=16 \Rightarrow x= \frac{16}{2} \Rightarrow \boxed{x=8}$

$\displaystyle f).3x+4- \frac{5x-9}{2} = \frac{3x+10}{4} - \frac{x-6}{2} \\ \\ 3x \cdot 4+4 \cdot 4-2(5x-9)=3x+10-2(x-6) \\ \\ 12x+16-10x+18=3x+10-2x+12 \\ \\ 12x-10x-3x+2x=10+12-16-18 \\ \\ \boxed{x=-12}$