\(21-\left(2x-4\right)\left(x+1\right)\)

\(=21-2x^2-2x+4x+4\)

\(=-2x^2+2x+25\)

a: \(\left|-x+\frac25\right|+\frac12=3,5\)

=>\(\left|x-\frac25\right|=3,5-0,5=3\)

=>\(\left[\begin{array}{l}x-\frac25=3\\ x-\frac25=-3\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3+\frac25=\frac{17}{5}\\ x=-3+\frac25=-\frac{13}{5}\end{array}\right.\)

b: \(\frac{21}{5}+3:\left|\frac{x}{4}-\frac23\right|=6\)

=>\(3:\left|\frac14x-\frac23\right|=6-\frac{21}{5}=\frac95\)

=>\(\left|\frac14x-\frac23\right|=3:\frac95=3\cdot\frac59=\frac53\)

=>\(\left[\begin{array}{l}\frac14x-\frac23=\frac53\\ \frac14x-\frac23=-\frac53\end{array}\right.\Rightarrow\left[\begin{array}{l}\frac14x=\frac23+\frac53=\frac73\\ \frac14x=-\frac53+\frac23=-\frac33=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac73\cdot4=\frac{28}{3}\\ x=-1\cdot4=-4\end{array}\right.\)

c: 7,5-3|5-2x|=-4,5

=>3|5-2x|=7,5+4,5=12

=>3|2x-5|=12

=>|2x-5|=4

=>\(\left[\begin{array}{l}2x-5=4\\ 2x-5=-4\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=9\\ 2x=1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac92\\ x=\frac12\end{array}\right.\)

d: \(\frac13-\left|\frac54-2x\right|=\frac14\)

=>\(\left|\frac54-2x\right|=\frac13-\frac14=\frac{1}{12}\)

=>\(\left|2x-\frac54\right|=\frac{1}{12}\)

=>\(\left[\begin{array}{l}2x-\frac54=\frac{1}{12}\\ 2x-\frac54=-\frac{1}{12}\end{array}\right.\Rightarrow\left[\begin{array}{l}2x=\frac54+\frac{1}{12}=\frac{16}{12}=\frac43\\ 2x=\frac54-\frac{1}{12}=\frac{15}{12}-\frac{1}{12}=\frac{14}{12}=\frac76\end{array}\right.\)

=>\(\left[\begin{array}{l}x=\frac23\\ x=\frac{7}{12}\end{array}\right.\)

e: \(\frac{21}{5}+3:\left|\frac{x}{4}-\frac23\right|=6\)

=>\(3:\left|\frac14x-\frac23\right|=6-\frac{21}{5}=\frac95\)

=>\(\left|\frac14x-\frac23\right|=3:\frac95=3\cdot\frac59=\frac53\)

=>\(\left[\begin{array}{l}\frac14x-\frac23=\frac53\\ \frac14x-\frac23=-\frac53\end{array}\right.\Rightarrow\left[\begin{array}{l}\frac14x=\frac23+\frac53=\frac73\\ \frac14x=-\frac53+\frac23=-\frac33=-1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=\frac73\cdot4=\frac{28}{3}\\ x=-1\cdot4=-4\end{array}\right.\)

a: Ta có: \(\left|\dfrac{2}{5}-x\right|+\dfrac{1}{2}=3.5\)

\(\Leftrightarrow\left|x-\dfrac{2}{5}\right|=3\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{2}{5}=3\\x-\dfrac{2}{5}=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{17}{5}\\x=-\dfrac{13}{5}\end{matrix}\right.\)

b: Ta có: \(\dfrac{21}{5}+3:\left|\dfrac{x}{4}-\dfrac{2}{3}\right|=6\)

\(\Leftrightarrow3:\left|\dfrac{1}{4}x-\dfrac{2}{3}\right|=6-\dfrac{21}{5}=\dfrac{9}{5}\)

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

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{4}x-\dfrac{2}{3}=\dfrac{5}{3}\\\dfrac{1}{4}x-\dfrac{2}{3}=-\dfrac{5}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{4}x=\dfrac{7}{3}\\\dfrac{1}{4}x=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{28}{3}\\x=-4\end{matrix}\right.\)

em muốn hỏi là tại sao 3,5 bên trên xuống dưới lại là 3 và -x +2/5 của em xuống dưới lại chuyển thành x-2/5 ạ mong anh giải đáp

a)

ĐKXĐ: \(x\ne-4\)

Để A nguyên thì \(3x+21⋮x+4\)

\(\Leftrightarrow3x+12+9⋮x+4\)

mà \(3x+12⋮x+4\)

nên \(9⋮x+4\)

\(\Leftrightarrow x+4\inƯ\left(9\right)\)

\(\Leftrightarrow x+4\in\left\{1;-1;3;-3;9;-9\right\}\)

\(\Leftrightarrow x\in\left\{-3;-5;-1;-7;5;-13\right\}\)(nhận)

Vậy: Để A nguyên thì \(x\in\left\{-3;-5;-1;-7;5;-13\right\}\)

b) ĐKXĐ: \(x\ne\dfrac{1}{2}\)

Để B nguyên thì \(2x^3-7x^2+7x+5⋮2x-1\)

\(\Leftrightarrow2x^3-x^2-6x^2+3x+4x-2+7⋮2x-1\)

\(\Leftrightarrow x^2\left(2x-1\right)-3x\left(2x-1\right)+2\left(2x-1\right)+7⋮2x-1\)

\(\Leftrightarrow\left(2x-1\right)\left(x^2-3x+2\right)+7⋮2x-1\)

mà \(\left(2x-1\right)\left(x^2-3x+2\right)⋮2x-1\)

nên \(7⋮2x-1\)

\(\Leftrightarrow2x-1\inƯ\left(7\right)\)

\(\Leftrightarrow2x-1\in\left\{1;-1;7;-7\right\}\)

\(\Leftrightarrow2x\in\left\{2;0;8;-6\right\}\)

hay \(x\in\left\{1;0;4;-3\right\}\)(nhận)

Vậy: \(x\in\left\{1;0;4;-3\right\}\)

a) | 5/4x -7/2| - | 5/8x + 3/5| = 0

|5/4x - 7/2| = | 5/8x + 3/5|

TH1: 5/4x - 7/2 = 5/8x + 3/5

=> 5/4x - 5/8x = 3/5 +7/2

5/8x = 41/10

x = 41/10:5/8

x = 164/25

TH2: 5/4x - 7/2 = -5/8x - 3/5

=> 5/4x + 5/8x  = -3/5 +7/2

15/8x  = 29/10

x = 29/10 : 15/8

x = 116/75

KL: x = 164/25 hoặc x = 116/75

các bài cn lại b lm tương tự nha! h lm dài lắm!

Chỗ câu b ý, 3³ = 27 mà ta :))

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