Question

\(|x-\frac{1}{6}|-\frac{6}{16}=25\%\)

Answer 1

I x - 1/6 I - 6/16 = 25%

=> I x - 1/6 I- 6/16 = 1/4

=>I x - 1/6 I = 5/8

\(\Rightarrow\orbr{\begin{cases}x-\frac{1}{6}=\frac{5}{8}\\x-\frac{1}{6}=-\frac{5}{8}\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{19}{24}\\x=-\frac{11}{24}\end{cases}}\)

vậy x = 19/24 , x = -11/24

Answer 2

\(\left|x-\frac{1}{6}\right|-\frac{6}{16}=25\%\)

\(\left|x-\frac{1}{6}\right|-\frac{3}{8}=\frac{2}{8}\)

\(\left|x-\frac{1}{6}\right|=\frac{2}{8}+\frac{3}{8}\)

\(\left|x-\frac{1}{6}\right|=\frac{5}{8}\)

=> 2 trường hợp:

1 là \(x-\frac{1}{6}=\frac{5}{8}\)

2 là \(x-\frac{1}{6}=\frac{-5}{8}\)

Trường hợp 1:\(x=\frac{5}{8}+\frac{1}{6}=\frac{19}{24}\)

Trường hợp 2:\(x=\frac{-5}{8}+\frac{1}{6}=\frac{-11}{24}\)

Hội con 🐄 chúc bạn học tốt!!!

Answer 3

|x - 1/6| - 6/16 = 25%

|x - 1/6| - 3/8 = 0,25

|x - 1/6| = 0,25 + 3/8

|x - 1/6| = 5/8

x - 1/6 = 5/8 hoặc x - 1/6 = -5/8

x = 5/8 + 1/6         x = -5/8 + 1/6

x =19/24               x = -11/24

Answer 4

| x - 1 / 6 |  - 6 / 16 = 25 % 

=> | x - 1 / 6 |  - 3 / 8 = 1 / 4

=> | x - 1 / 6 | = 2 / 8 + 3 / 8

=> | x - 1 / 6 | = 5 / 8

=> x - 1 / 6 = 5 / 8 ; x - 1 / 6 = -5 / 8

=> x = 5 / 8 + 1 / 6 ; x = -5 / 8 + 1 / 6

=> x = 19 / 24 ; x = -11 / 24

Answer 5

\(|x-\frac{1}{6}|-\frac{6}{16}=25\%\)

\(\Rightarrow|x-\frac{1}{6}|=\frac{25}{100}+\frac{6}{16}\)

\(\Rightarrow|x-\frac{1}{6}|=\frac{1}{4}+\frac{3}{8}\)

\(\Rightarrow|x-\frac{1}{6}|=\frac{5}{8}\)

Với \(x\ge\frac{1}{6}\Rightarrow x-\frac{1}{6}=\frac{5}{8}\)

\(\Rightarrow x=\frac{5}{8}+\frac{1}{6}=\frac{15}{24}+\frac{4}{24}=\frac{29}{24}\left(tm\right)\)

Với \(x< \frac{1}{6}\Rightarrow x-\frac{1}{6}=-\frac{5}{8}\)

\(\Rightarrow x=-\frac{5}{8}+\frac{1}{6}=-\frac{15}{24}+\frac{4}{24}=-\frac{11}{24}\left(tm\right)\)

Vậy \(x\in\left\{\frac{29}{24};-\frac{11}{24}\right\}\)

Answer 6

\(\left|x-\frac{1}{6}\right|-\frac{6}{16}=25\%\)

\(\Leftrightarrow\left|x-\frac{1}{6}\right|-\frac{3}{8}=\frac{1}{4}\)

\(\Leftrightarrow\left|x-\frac{1}{6}\right|=\frac{1}{4}+\frac{3}{8}=\frac{5}{8}\)

Trường hợp 1 : Xét \(x-\frac{1}{6}>0\)hay x > 1/6

Ta có : \(x-\frac{1}{6}=\frac{5}{8}\)

\(\Leftrightarrow x=\frac{5}{8}+\frac{1}{6}\)

\(\Leftrightarrow x=\frac{15}{24}+\frac{4}{24}=\frac{19}{24}\)

nhận vì \(\frac{19}{24}>\frac{1}{6}\)hay \(\frac{19}{24}>\frac{4}{24}\)

Trường hợp 2 : Xét \(x-\frac{1}{6}< 0\)=> x < 1/6

Ta có : \(x-\frac{1}{6}=-\frac{5}{8}\)

=> \(x=-\frac{5}{8}+\frac{1}{6}=-\frac{11}{24}\)

nhận vì \(-\frac{11}{24}< \frac{1}{6}\)