Bonsoir Aniaslimani
Exercice 29
[tex]a)\ 3x-\dfrac{1}{2}=-\dfrac{3}{4}-5x\\\\3x+5x=-\dfrac{3}{4}+\dfrac{1}{2}\\\\8x=-\dfrac{3}{4}+\dfrac{2}{4}\\\\8x=-\dfrac{1}{4}\\\\x=\dfrac{1}{8}\times(-\dfrac{1}{4})\\\\\boxed{x=-\dfrac{1}{32}}[/tex]
[tex]b)\ \dfrac{1}{4}x+\dfrac{5}{2}=-x+1\\\\\dfrac{1}{4}x+x=1-\dfrac{5}{2}\\\\\dfrac{1}{4}x+\dfrac{4}{4}x=\dfrac{2}{2}-\dfrac{5}{2}\\\\\dfrac{5}{4}x=-\dfrac{3}{2}\\\\x=-\dfrac{3}{2}\times\dfrac{4}{5}}\\\\x=-\dfrac{12}{10}[/tex]
[tex]\\\\\boxed{x=-\dfrac{6}{5}}[/tex]
[tex]c)\ -\dfrac{4}{5}+y=\dfrac{3}{10}-\dfrac{1}{2}y\\\\y+\dfrac{1}{2}y=\dfrac{3}{10}+\dfrac{4}{5}\\\\\dfrac{2}{2}y+\dfrac{1}{2}y=\dfrac{3}{10}+\dfrac{8}{10}\\\\\dfrac{3}{2}y=\dfrac{11}{10}
\\\\y=\dfrac{11}{10}\times\dfrac{2}{3}\\\\y=\dfrac{22}{30}
[/tex]
[tex]\boxed{y=\dfrac{11}{15}}
[/tex]
[tex]d)\ \dfrac{5}{2}a+\dfrac{1}{4}=\dfrac{1}{4}a+\dfrac{2}{5}\\\\\dfrac{5}{2}a-\dfrac{1}{4}a=\dfrac{2}{5}-\dfrac{1}{4}\\\\\dfrac{10}{4}a-\dfrac{1}{4}a=\dfrac{8}{20}-\dfrac{5}{20}\\\\\dfrac{9}{4}a=\dfrac{3}{20}\\\\a=\dfrac{3}{20}\times\dfrac{4}{9}\\\\\boxed{a=\dfrac{1}{15}}[/tex]
Exercice 30
[tex]A)\ \dfrac{5-2x}{4}=3x-1\\\\\dfrac{5}{4}-\dfrac{2}{4}x=3x-1\\\\\dfrac{5}{4}-\dfrac{1}{2}x=3x-1\\\\-\dfrac{1}{2}x-3x=-1-\dfrac{5}{4}\\\\-\dfrac{1}{2}x-\dfrac{6}{2}x=-\dfrac{4}{4}-\dfrac{5}{4}\\\\-\dfrac{7}{2}x=-\dfrac{9}{4}[/tex]
[tex]\\\\x=(-\dfrac{9}{4})\times(-\dfrac{2}{7})\\\\\boxed{x=\dfrac{9}{14}}[/tex]
[tex]B)\ \dfrac{2}{5}+t=\dfrac{1}{4}t+1\\\\t-\dfrac{1}{4}t=1-\dfrac{2}{5}\\\\\dfrac{4}{4}t-\dfrac{1}{4}t=\dfrac{5}{5}-\dfrac{2}{5}\\\\\dfrac{3}{4}t=\dfrac{3}{5}\\\\t=\dfrac{3}{5}\times\dfrac{4}{3}\\\\\boxed{t=\dfrac{4}{5}}[/tex]
[tex]C)\ \dfrac{1}{4}y-3=\dfrac{3}{2}y+1\\\\\dfrac{1}{4}y-\dfrac{3}{2}y=1+3\\\\\dfrac{1}{4}y-\dfrac{6}{4}y=4
\\\\-\dfrac{5}{4}y=4\\\\y=4\times(-\dfrac{4}{5})\\\\\boxed{y=-\dfrac{16}{5}}[/tex]
[tex]D)\ \dfrac{1}{3}m+6=\dfrac{4}{3}-2m\\\\\dfrac{1}{3}m+2m=\dfrac{4}{3}-6\\\\\dfrac{1}{3}m+\dfrac{6}{3}m=\dfrac{4}{3}-\dfrac{18}{3}\\\\\dfrac{7}{3}m=-\dfrac{14}{3}\\\\m=-\dfrac{14}{3}\times\dfrac{3}{7}\\\\\boxed{m=-2}[/tex]
Aline dit vrai (voir l'équation D où m = -2 qui est un nombre entier)
Léonard dit vrai (voir l'équation C où y = -16/5 = -3,2 qui est un nombre décimal)
Maggy dit vrai (voir l'équation A où x = 9/14 ≈ 0,6428571429... qui est un nombre non décimal)
