vẫn dùng nick này à

Tìm x biết:

| 3 - x | = x - 5

Giải:

Ta có: \(3-x=x-5\) hoặc \(3-x=-\left(x-5\right)\)

\(TH1:3-x=x-5\)

\(2x=3+5\)

\(2x=8\)

\(\Rightarrow x=4\)

\(TH2:3-x=-\left(x-5\right)\)

\(3-x=-x+5\)

\(-x-x=5-3\)

\(2.\left(-x\right)=2\)

\(-x=1\)

\(\Rightarrow x=-1\)

mk sư tử nhé

Cho \(A=\dfrac{\dfrac{-5}{8}.\dfrac{3}{7}+\dfrac{3}{7}.\dfrac{3}{4}+\dfrac{1}{7}.\dfrac{1}{2}+\dfrac{15}{8}}{a+\dfrac{5}{6}-\left(\dfrac{-1}{3}\right)}\)

a) Rút gọn A?

b) Tính A khi a=75%

c) Tìm a để A=50%

d) Tìm a thuộc Z để A là số nguyên.

e) Với a = bao nhiêu để A có giá trị bằng với giá trị của biểu thức:

\(B=\dfrac{\dfrac{2}{3}.\dfrac{15}{6}+\left(-0,5\right)^3}{\dfrac{1}{9}.6^2-5\dfrac{1}{3}}\)

Giải

a, Ta có:

\(A=\dfrac{\dfrac{-5}{8}.\dfrac{3}{7}+\dfrac{3}{7}.\dfrac{3}{4}+\dfrac{3}{7}.\dfrac{1}{6}+\dfrac{1}{8}.15}{a+\dfrac{5}{6}+\dfrac{1}{3}}\)

\(A=\dfrac{\dfrac{3}{7}.\left(\dfrac{-5}{8}+\dfrac{3}{4}+\dfrac{1}{6}\right)+\dfrac{1}{8}.15}{a+\dfrac{7}{6}}\)

\(A=\dfrac{\dfrac{3}{7}.\dfrac{7}{24}+\dfrac{1}{8}.15}{a+\dfrac{7}{6}}\)

\(A=\dfrac{\dfrac{1}{8}+\dfrac{1}{8}.15}{a+\dfrac{7}{6}}\)

\(A=\dfrac{\dfrac{1}{8}.\left(15+1\right)}{a+\dfrac{7}{6}}\)

\(A=\dfrac{2}{a+\dfrac{7}{6}}\)

b, Thay \(a=75\%\) vào \(A\), ta được:

\(A=\dfrac{2}{75\%+\dfrac{7}{6}}\)

\(A=\dfrac{2}{\dfrac{3}{4}+\dfrac{7}{6}}\)

\(\Rightarrow A=\dfrac{23}{12}\)

c, Ta có: \(\dfrac{2}{a+\dfrac{7}{6}}=50\%\)

\(\dfrac{2}{a+\dfrac{7}{6}}=\dfrac{1}{2}\)

\(\dfrac{2}{a+\dfrac{7}{6}}=\dfrac{2}{4}\)

\(\Rightarrow a+\dfrac{7}{6}=4\)

\(\Rightarrow a=\dfrac{17}{6}\)

d, Để \(A\in Z\Rightarrow2⋮a+\dfrac{7}{6}\)

\(\Rightarrow a+\dfrac{7}{6}\in\left\{\pm1;\pm2\right\}\)

\(\circledast,a+\dfrac{7}{6}=1\Rightarrow a=\dfrac{-1}{6}\)

\(\circledast,a+\dfrac{7}{6}=-1\Rightarrow a=\dfrac{-13}{6}\)

\(\circledast,a+\dfrac{7}{6}=2+\Rightarrow a=\dfrac{5}{6}\)

\(\circledast,a+\dfrac{7}{6}=-2\Rightarrow a=\dfrac{-19}{6}\)

\(a\in\varnothing\) khi \(A\in Z\)

e, Ta có:

\(B=\dfrac{5}{3}+\dfrac{-1}{8}\Rightarrow B=\dfrac{37}{24}\)

\(\Rightarrow\dfrac{2}{a+\dfrac{7}{6}}=\dfrac{37}{24}\)

\(a+\dfrac{7}{6}=\dfrac{37}{24}.2\)

\(a+\dfrac{7}{6}=\dfrac{37}{12}\)

\(\Rightarrow a=\dfrac{23}{12}\)

Chúc bạn học thiệt giỏi nha!!!

Đẹp . Nhất là hình Mizuki.