Question

Bài 1: Tìm x:

a) \(\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)

b) \(\left|\dfrac{5}{3}x\right|=\left|-\dfrac{1}{6}\right|\)

c) \(\left|\dfrac{3}{4}x-\dfrac{3}{4}\right|-\dfrac{3}{4}=\left|-\dfrac{3}{4}\right|\)

Bài 2: Tìm x,y:

a) \(\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|=\dfrac{1}{4}-\left|y\right|\)

b) \(\left|x-y\right|+\left|y+\dfrac{9}{25}\right|=0\)

Bài 3: Tìm giá trị nhỏ nhất:

a) A= \(\left|x+\dfrac{15}{19}\right|-1\)

b) B= \(\dfrac{1}{2}+\left|x-\dfrac{4}{7}\right|\)

Bài 4: Tìm giá trị lớn nhất:

a) A= 5- \(\left|\dfrac{5}{3}-x\right|\)

b) B= 9-\(\left|x-\dfrac{1}{10}\right|\)

Answer 1

Bài 1: 

a: \(\Leftrightarrow\left|x+\dfrac{4}{15}\right|=-2.15+3.75=\dfrac{8}{5}\)

=>x+4/15=8/5 hoặc x+4/15=-8/5

=>x=4/3 hoặc x=-28/15

b: \(\Leftrightarrow\left[{}\begin{matrix}\dfrac{5}{3}x=-\dfrac{1}{6}\\\dfrac{5}{3}x=\dfrac{1}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-1}{6}:\dfrac{5}{3}=\dfrac{-3}{30}=\dfrac{-1}{10}\\x=\dfrac{1}{10}\end{matrix}\right.\)

c: \(\Leftrightarrow\left|x-1\right|-1=1\)

=>|x-1|=2

=>x-1=2 hoặc x-1=-2

=>x=3 hoặc x=-1

Bài 2: 

b: \(\Leftrightarrow\left\{{}\begin{matrix}x-y=0\\y+\dfrac{9}{25}=0\end{matrix}\right.\Leftrightarrow x=y=-\dfrac{9}{25}\)

Bài 3: 

a: \(A=\left|x+\dfrac{15}{19}\right|-1>=-1\)

Dấu '=' xảy ra khi x=-15/19

b: \(\left|x-\dfrac{4}{7}\right|+\dfrac{1}{2}>=\dfrac{1}{2}\)

Dấu '=' xảy ra khi x=4/7