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\(\Leftrightarrow4+56x=25-15x\)

=>71x=21

hay x=21/71

a = |2x-1/3|-7/4

   Do |2x-1/3| \(\ge\) 0

         |2x-1/3|-7/4 \(\ge\)  7/4 

Dấu = xảy ra <=> 2x-1/3=0. =>. x= 1/6

b    1/3|x-2|+2|3-1/2 y|+4

 Do |x-2| \(\ge\) 0

      |3-1/2y| \(\ge\) 0

   => 1/3|x-2|+2|3-1/2 y|+4 \(\ge\) 4

Dấu = xảy ra <=>\(\left\{{}\begin{matrix}x-2=0\\3-\dfrac{1}{2}y=0\end{matrix}\right.\)

<=>\(\left\{{}\begin{matrix}x=2\\y=6\end{matrix}\right.\)

a: Ta có: \(\left|2x-\dfrac{1}{3}\right|\ge0\forall x\)

\(\Leftrightarrow\left|2x-\dfrac{1}{3}\right|-\dfrac{7}{4}\ge-\dfrac{7}{4}\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{1}{6}\)

b: Ta có: \(\dfrac{1}{3}\left|x-2\right|\ge0\forall x\)

\(2\left|3-\dfrac{1}{2}y\right|\ge0\forall y\)

Do đó: \(\dfrac{1}{3}\left|x-2\right|+2\left|3-\dfrac{1}{2}y\right|\ge0\forall x,y\)

\(\Leftrightarrow\left|x-2\right|\cdot\dfrac{1}{3}+\left|3-\dfrac{1}{2}y\right|\cdot2+4\ge4\forall x,y\)

Dấu '=' xảy ra khi x=2 và y=6

\(\dfrac{x-7}{y-6}=\dfrac{7}{6}\\ \Leftrightarrow6x-42=7y-42\\ \Leftrightarrow6x=7y\\ \Leftrightarrow\dfrac{x}{7}=\dfrac{y}{6}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{7}=\dfrac{y}{6}=\dfrac{x-y}{7-6}=\dfrac{-4}{1}=-4\\ \dfrac{x}{7}=-4\Leftrightarrow x=-28\\ \dfrac{y}{6}=-4\Leftrightarrow y=-24\)

\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(\dfrac{1}{3}-\dfrac{5}{4}\right)-\left(\dfrac{2}{7}+\dfrac{1}{3}\right)\right]\right\}\)

\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\left[\dfrac{15}{21}-\left(-\dfrac{11}{12}\right)-\dfrac{13}{21}\right]\right\}\)

\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left\{\dfrac{7}{12}-\dfrac{85}{84}\right\}\)

\(B=\dfrac{3}{2}-\dfrac{2}{21}-\left(-\dfrac{3}{7}\right)\)

\(B=\dfrac{11}{6}\)

\(=\dfrac{3}{2}-\dfrac{2}{21}-\dfrac{7}{12}+\left[\dfrac{15}{21}-\dfrac{1}{3}+\dfrac{5}{4}-\dfrac{2}{7}-\dfrac{1}{3}\right]\)

=11/12-2/21+5/7-2/3+5/4-2/7

=11/12-2/3+5/4-2/21+3/7

=11/12-8/12+15/12-2/21+9/21

=18/12+7/21

=3/2+1/3

=9/6+2/6=11/6

a) |2x-3|+x=21

|2x-3|=21-x

\(\Rightarrow\)\(\orbr{\begin{cases}2x-3=21-x\\2x-3=-\left(21-x\right)\end{cases}}\)

TH1: 2x-3=21-x

2x-x=21+3

x=24

TH2: 2x-3=-(21-x)

2x-3 = -21+x

2x-x=-21+3

x=-18

Vậy x \(\varepsilon\){-18;24}