Bài 4: Giá trị tuyệt đối của một số hữu tỉ. Cộng, trừ, nhân, chia số thập phân

|a|=|b|

=>\(\left[{}\begin{matrix}a=b\\a=-b\end{matrix}\right.\)

|x+1,2|-|2,4-x|=0

=>\(\left|x+1,2\right|=\left|2,4-x\right|\)

=>\(\left[{}\begin{matrix}x+1,2=2,4-x\\x+1,2=x-2,4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x+x=2,4-1,2\\0x=-3,6\left(loại\right)\end{matrix}\right.\)

=>2x=1,2

=>\(x=1,2:2=0,6\)

\(\left|x-\dfrac{1}{2}\right|+\dfrac{3}{4}=\dfrac{9}{10}\)

=>\(\left|x-\dfrac{1}{2}\right|=\dfrac{9}{10}-\dfrac{3}{4}=\dfrac{3}{20}\)

=>\(\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{3}{20}\\x-\dfrac{1}{2}=-\dfrac{3}{20}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{20}+\dfrac{1}{2}=\dfrac{13}{20}\\x=-\dfrac{3}{20}+\dfrac{1}{2}=\dfrac{7}{20}\end{matrix}\right.\)

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

=>\(\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{3}{2}\\x-\dfrac{1}{2}=-\dfrac{3}{2}\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=\dfrac{3}{2}+\dfrac{1}{2}=\dfrac{4}{2}=2\\x=-\dfrac{3}{2}+\dfrac{1}{2}=-\dfrac{2}{2}=-1\end{matrix}\right.\)

\(\left|x-\dfrac{1}{2}\right|=\dfrac{3}{2}\\ TH1:x-\dfrac{1}{2}=\dfrac{3}{2}\\ x=\dfrac{3}{2}+\dfrac{1}{2}=2\\ TH2:X-\dfrac{1}{2}=-\dfrac{3}{2}\\ x=-\dfrac{3}{2}+\dfrac{1}{2}=-1\)

\(\left|x-3\right|>=0\forall x\)

=>\(\left|x-3\right|+2>=2\forall x\)

=>\(\left(\left|x-3\right|+2\right)^2>=2^2=4\forall x\)

Ta có: \(\left(\left|x-3\right|+2\right)^2>=4\forall x\)

\(\left|y+3\right|>=0\forall y\)

Do đó: \(\left(\left|x-3\right|+2\right)^2+\left|y+3\right|>=4+0=4\forall x,y\)

=>\(\left(\left|x-3\right|+2\right)^2+\left|y+3\right|+2018>=4+2018=2022\forall x,y\)

=>\(P>=2022\forall x,y\)

Dấu '=' xảy ra khi x-3=0 và y+3=0

=>\(\left\{{}\begin{matrix}x=3\\y=-3\end{matrix}\right.\)

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

=>\(\left|x-\dfrac{1}{3}\right|+0,8=\left|-3,2+0,4\right|=2,8\)

=>\(\left|x-\dfrac{1}{3}\right|=2,8-0,8=2\)

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

Lời giải:

$|-5,5|=5,5$ nên số đối của nó là $-5,5$

$|\frac{3}{8}|=\frac{3}{8}$ nên số đối của nó là $\frac{-3}{8}$

$|\frac{-7}{11}|=\frac{7}{11}$ nên số đối của nó là $\frac{-7}{11}$

Lời giải:

$|2x+5|+|3x-7|=5|3x-7|$

$\Rightarrow |2x+5|=4|3x-7|$

$\Rightarrow 2x+5=4(3x-7)$ hoặc $2x+5=-4(3x-7)$

Nếu $2x+5=4(3x-7)$

$\Rightarrow 2x+5=12x-28$

$\Rightarrow 33=10x$

$\Rightarrow x=\frac{33}{10}$

Nếu $2x+5=-4(3x-7)$

$\Leftrightarrow 2x+5=-12x+28$

$\Leftrightarrow 14x=23$

$\Leftrightarrow x=\frac{23}{14}$

Là đúng

Đúng

\(\left|-3,2\right|=3,2;\left|1,7\right|=1,7\)

\(\left|-4.5\right|=4.5;\left|-21\right|=21;\left|-3.5\right|=3.5\)