Ta có \(M=\frac{2a+8}{5}+\frac{-a-7}{5}=\frac{2a+8-a-7}{5}=\frac{a+1}{5}\)

Để \(M\inℤ\Leftrightarrow\frac{a+1}{5}\inℤ\Leftrightarrow a+1⋮5\Leftrightarrow a+1\inƯ\left(5\right)=\left\{\pm1;\pm5\right\}\)

Ta có bảng sau :

Vậy \(a\in\left\{0;-2;4;-6\right\}\)

Đặt \(A=\frac{1}{31}+\frac{1}{32}+...+\frac{1}{90}\)

         \(=\left(\frac{1}{31}+\frac{1}{32}+...+\frac{1}{45}\right)+\left(\frac{1}{46}+\frac{1}{47}+...+\frac{1}{90}\right)\)

Đặt \(B=\frac{1}{31}+\frac{1}{32}+...+\frac{1}{45}\)

 Ta có: \(\frac{1}{31}>\frac{1}{45}\)

           \(\frac{1}{32}>\frac{1}{45}\)

           ....................

          \(\frac{1}{45}=\frac{1}{45}\)

\(\Rightarrow B>\frac{1}{45}.15\)

\(\Rightarrow B>\frac{1}{3}\)

Đặt \(C=\frac{1}{46}+\frac{1}{47}+...+\frac{1}{90}\)

Ta có: \(\frac{1}{46}>\frac{1}{90}\)

           \(\frac{1}{47}>\frac{1}{90}\)

          .....................

         \(\frac{1}{90}=\frac{1}{90}\)

\(\Rightarrow C>\frac{1}{90}.45\)

\(\Rightarrow C>\frac{1}{2}\)

\(\Rightarrow B+C>\frac{1}{3}+\frac{1}{2}\)

Hay \(A>\frac{5}{6}\left(1\right)\)

Lại có: \(A=\left(\frac{1}{31}+...+\frac{1}{59}\right)+\left(\frac{1}{60}+...+\frac{1}{90}\right)\)

Đặt \(D=\frac{1}{31}+...+\frac{1}{59}\)

Ta có: \(\frac{1}{31}< \frac{1}{30}\)

          . ...................

           \(\frac{1}{59}< \frac{1}{30}\)

\(\Rightarrow D< \frac{1}{30}.60\)

\(\Rightarrow D< \frac{1}{2}\)

Đăt \(E=\frac{1}{60}+...+\frac{1}{90}\)

Ta có: \(\frac{1}{60}=\frac{1}{60}\)

             .................

          \(\frac{1}{90}< \frac{1}{60}\)

\(\Rightarrow E< \frac{1}{60}.31\)

\(\Rightarrow E< \frac{31}{60}< 1\)

\(\Rightarrow E< 1\)

\(\Rightarrow E+D< 1+\frac{1}{2}\)

Hay \(A< \frac{3}{2}\left(2\right)\)

Từ (1) và (2) \(\Rightarrow\frac{5}{6}< A< \frac{3}{2}\)

Mình làm hơi ngáo có gì thì cứ nói 

\(\left(4,5+2x\right)\div\frac{3}{4}=-1\frac{1}{3}\)

\(\Leftrightarrow\left(4,5+2x\right)\div\frac{3}{4}=-\frac{4}{3}\)

\(\Leftrightarrow4,5+2x=-\frac{4}{3}\times\frac{3}{4}\)

\(\Leftrightarrow4,5+2x=-1\)

\(\Leftrightarrow2x=-1-4,5\)
\(\Leftrightarrow2x=-5,5\)

\(\Leftrightarrow x=-5,5\div2\)

\(\Leftrightarrow x=-2,75\)

\(A=\frac{-2}{4}+\frac{2}{7}-\frac{5}{28}\)

\(\Rightarrow A=\frac{-14}{28}+\frac{8}{28}-\frac{5}{28}\)

\(\Rightarrow A=\frac{-6}{28}-\frac{5}{28}\)

\(\Rightarrow A=\frac{-11}{28}\)

\(B=\frac{-7}{9}.\frac{4}{11}+\frac{-7}{9}.\frac{7}{5}+5.\frac{7}{9}\)

\(\Rightarrow B=\frac{-7}{9}.\frac{4}{11}+\frac{-7}{9}.\frac{7}{5}-5.\frac{-7}{9}\)

\(\Rightarrow B=\frac{-7}{9}.\left(\frac{4}{11}+\frac{7}{11}-5\right)\)

\(\Rightarrow B=\frac{-7}{9}.\left(1-5\right)\)

\(\Rightarrow B=\frac{-7}{9}.\left(-4\right)\)

\(\Rightarrow B=\frac{-28}{9}\)

\(-5\left(x+\frac{1}{5}\right)-\frac{1}{2}\left(x-\frac{2}{3}\right)=\frac{3}{2}x-\frac{5}{6}\)

\(\Leftrightarrow-5x-\frac{1}{5}-\frac{1}{2}x+\frac{1}{3}=\frac{3}{2}x-\frac{5}{6}\)

\(\Leftrightarrow\left(-5x-\frac{1}{2}x\right)+\left(\frac{1}{3}-\frac{1}{5}\right)=\frac{3}{2}x-\frac{5}{6}\)

\(\Leftrightarrow\left(\frac{-10}{2}x-\frac{1}{2}x\right)+\left(\frac{5}{15}-\frac{3}{15}\right)=\frac{3}{2}x-\frac{5}{6}\)

\(\Leftrightarrow\frac{-11}{2}x+\frac{2}{15}=\frac{3}{2}x-\frac{5}{6}\)

\(\Leftrightarrow\frac{-11}{2}x-\frac{3}{2}x=-\frac{5}{6}-\frac{2}{15}\)

\(\Leftrightarrow\frac{-14}{2}x=-\frac{25}{30}-\frac{4}{30}\)

\(\Leftrightarrow-7x=-\frac{29}{30}\)

\(\Leftrightarrow x=-\frac{29}{30}\times\frac{-1}{7}\)

\(\Leftrightarrow x=\frac{29}{210}\)

\(3\left(x-\frac{1}{2}\right)-5\left(x+\frac{3}{5}\right)=-x+\frac{1}{5}\)

\(\Leftrightarrow3x-\frac{3}{2}-5x-3=\frac{1}{5}-x\)

\(\Leftrightarrow\left(3x-5x\right)-\left(\frac{3}{2}+3\right)=\frac{1}{5}-x\)

\(\Leftrightarrow-2x-\left(\frac{3}{2}+\frac{6}{2}\right)=\frac{1}{5}-x\)

\(\Leftrightarrow-2x-\frac{9}{2}=\frac{1}{5}-x\)

\(\Leftrightarrow-2x+x=\frac{1}{5}+\frac{9}{2}\)

\(\Leftrightarrow-x=\frac{2}{10}+\frac{45}{10}\)

\(\Leftrightarrow-x=\frac{47}{10}\)

\(\Leftrightarrow x=\frac{-47}{10}\)

Câu 1 : 

Nhu cầu dinh dưỡng của cơ thể con người : 

+) Chất đạm 

+) Chất đường bột 

+) Chất béo

Câu 2 :

Trong gia đình bố mẹ thường là người chịu trách nhiệm tích lũy 

Chúc bạn học tốt mai thi