1/4 - 5/2 x |3x - 1/5|=2/3 x |3x - 1/5|- 2/3

Tương đương với 1/4+2/3 = 2/3 x l3x - 1/5l + 5/2 x l3x-1/5l

                           11/12    = l3x - 1/5l x (2/3 + 5/2)

                            11/12  = l3x -1/5 l x 19/6

        => l3x - 1/5l = 11/12 : 19/6 = 11/38

  Xét 2 trường hợp:

      + 3x - 1/5 = 11/38 => 3x = 11/38 + 1/5 = 93/190 => x = 93/190 : 3 = 31/190

      + 3x - 1/5 = -11/38 => 3x = -11/38 + 1/5 = -17/190 => x = -17/190 : 3 = -17/570

1. Thu gọn biểu thức - Hoc24 làm rồi mà bạn?

1.

a) \(=x^2-6x+9+3x^2-15x=4x^2-21x+9\)

b) \(=9x^2+12x+4-x^2+9=8x^2+12x+13\)

2.

a) \(\Leftrightarrow x^2+8x+16-x^2+4-5=0\\ \Leftrightarrow8x=-15\\ \Leftrightarrow x=-\dfrac{15}{8}\)

b) \(\Leftrightarrow9x^2-6x+1-8x^2+12x-2x+3-5-x^2=0\\ \Leftrightarrow4x=1\\ \Leftrightarrow x=\dfrac{1}{4}\)

1,a,=x2−6x+8+3x2−15x=4x2−21x+8b,=9x2+12x+4−x2+9=8x2+12x+132,a,⇔x2+8x+16−x2+4=5⇔8x=−15⇔x=−158b,⇔9x2−6x+1−8x2−2x+12x+3−x2=5⇔4x=1⇔x=14

a) 3/2.|x - 5/3| - 4/5 = 4/3.|x - 5/3| + 1

<=> 3/2.|x - 5/3| = 4/3.|x - 5/3| + 1 + 4/5

<=> 3/2.|x - 5/3| = 9/5 + 4|x - 5/3|/3

<=> 3/2.|x - 5/3| - 4.|x - 5/3|/3 = 9/5

<=> |x - 5/3|/6 = 9/5

<=> |x - 5/3| = 9/5.6

<=> |x - 5/3| = 54/5

<=> x - 5/3 = 54/5 hoặc x - 5/3 = -54/5

       x = 54/5 + 5/3         x = -54/5 - 5/3

       x = 187/15              x = -137/15

b) 2.|3x + 1| = 1/3.|3x + 1| + 5

<=> 2.|3x + 1| - 1/3.|3x + 1| = 5

<=> 5/3.|3x + 1| = 5

<=> 5.|3x + 1| = 5.3

<=> 5.|3x + 1| = 15

<=> |3x + 1| = 15 : 5

<=> |3x + 1| = 3

       3x + 1 = 3 hoặc 3x + 1 = -3 

       3x = 3 - 1           3x = -3 - 1

       3x = 2                3x = -4

       x = 2/3               x = -4/3

=> x = 2/3 hoặc x = -4/3

c) làm tương tự câu a) mình hơi lời

Làm câu c) cho

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

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

\(\Leftrightarrow\frac{3}{12}+\frac{8}{12}=\left|3x-\frac{1}{5}\right|\left(\frac{2}{3}+\frac{5}{2}\right)\)

\(\Leftrightarrow\left|3x-\frac{1}{5}\right|\left(\frac{4}{6}+\frac{15}{6}\right)=\frac{11}{12}\)

\(\Leftrightarrow\frac{19}{6}\left|3x-\frac{1}{5}\right|=\frac{11}{12}\)

\(\Leftrightarrow\left|3x-\frac{1}{5}\right|=\frac{11}{12}.\frac{6}{19}\)

\(\Leftrightarrow\left|3x-\frac{1}{5}\right|=\frac{11}{38}\)

\(\Leftrightarrow\orbr{\begin{cases}3x-\frac{1}{5}=\frac{11}{38}\\3x-\frac{1}{5}=-\frac{11}{38}\end{cases}}\)

Giải tiếp nha

b: \(\Leftrightarrow4x+13=5\)

hay x=-2

a) 2x(3x+1) – (2x+3)(3x-2) = 12

\(\Leftrightarrow6x^2+2x-\left(6x^2-4x+9x-6\right)=12\)

\(\Leftrightarrow6x^2+2x-6x^2+4x-9x+6=12\)

\(\Leftrightarrow-3x+6=12\) 

\(\Leftrightarrow-3x=6\)  

\(\Leftrightarrow x=-2\)  

vậy x = -2

 b)  (x+2)² – (x-3)(x+3) = 5

\(\Leftrightarrow\left(x+2\right)^2-\left(x^2-9\right)=5\)

\(\Leftrightarrow x^2+4x+4-x^2+9-5=0\)  

\(\Leftrightarrow4x+8=0\)

\(\Leftrightarrow4x=-8\) 

\(\Leftrightarrow x=-2\)

Vậy  x = -2

\(a,2\left(x-1\right)-x\left(3-x\right)=x^2\)

    \(\Leftrightarrow2x-2-3x+x^2=x^2\)

      \(\Leftrightarrow\left(2x-3x\right)+\left(x^2-x^2\right)-2=0\)

    \(\Leftrightarrow-\left(x+2\right)=0\Leftrightarrow x+2=0\Leftrightarrow x=-2\)

\(b,3x\left(x+5\right)-2\left(x+5\right)=3x^2\)

\(\Leftrightarrow3x^2+15x-2x-10=3x^2\)

\(\Leftrightarrow\left(3x^2-3x^2\right)+\left(15x-2x\right)-10=0\)

\(\Leftrightarrow13x-10=0\Leftrightarrow13x=10\Leftrightarrow x=\frac{10}{13}\)

ta có :  2 ( x - 1 ) - x ( 3 - x ) = x^2

 =>      2x - 2 - 3x