a) [latex]- (8x - 6) = 5x - 12[/latex] [latex]- 8x + 6 = 5x - 12[/latex] [latex]- 8x-5x = - 12-6[/latex] [latex]- 13x = - 18 /:(-13)[/latex] [latex]x =1 frac{5}{13}[/latex] Spr.: [latex]L=-(8 cdot 1 frac{5}{13} -6)=-(8frac{40}{13} -6)=-2frac{40}{13}=-5 frac{1}{13}[/latex] [latex]P=5 cdot 1 frac{5}{13}-12=5frac{25}{13}-12=6frac{12}{13}-12=-5 frac{1}{13}[/latex] [latex]L=P[/latex] ================== b) [latex]- 3x + 4 = - (4x + 7)[/latex] [latex]- 3x + 4 = - 4x -7[/latex] [latex]- 3x + 4x = -7-4[/latex] [latex]x = -11[/latex] Spr.: [latex]L=-3 cdot (-11)+4=33+4=37[/latex] [latex]P=-(4 cdot (-11)+7)=-(-44+7)=-37[/latex] [latex]L=P[/latex] ================== c) [latex]- (x + 8) = 4x - 6[/latex] [latex]- x - 8 = 4x - 6[/latex] [latex]- x - 4x = - 6+8[/latex] [latex]- 5x = 2 /:(-5)[/latex] [latex]x=- frac{2}{5}[/latex] Spr.: [latex]L=-(- frac{2}{5}+8)=-7 frac{3}{5}[/latex] [latex]P=4 cdot left( - frac{2}{5} ight) -6=- frac{8}{5}-6=-6 frac{8}{5}=-7 frac{3}{5}[/latex] [latex]L=P[/latex] ================== d) [latex]frac{2x - 7}{6} = 4x - 2 / cdot 6[/latex] [latex]2x - 7 = 24x - 12[/latex] [latex]2x - 24x= - 12+7[/latex] [latex]- 22x= - 5 /:(-22)[/latex] [latex]x= frac{5}{22}[/latex] Spr.: [latex]L= frac{2 cdot frac{5}{22}-7}{6}= frac{frac{5}{11}-7}{6}= frac{-6frac{6}{11}}{6}= -frac{72}{11} cdot frac{1}{6} =- frac{12}{11}=-1 frac{1}{11}[/latex] [latex]P=4 cdot frac{5}{22}-2= frac{10}{11}-2=-1 frac{1}{11}[/latex] [latex]L=P[/latex]
