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Câu a:
- |- 5 + 3 - 7| - |- 5 + 7|
= -|- 2 - 7| - |2|
= - |-9| - 2
= - 9 - 2
= -11
Câu b:
24 - (72 - 13 + 24) - (72 - 13)
= 24 - 72 + 13 - 24 - 72 + 13
= (24 - 24) - (72 + 72) + (13 + 13)
= 0 - 144 + 26
= - 118
Câu c:
|4 - 9 - 5| - (4 - 9 - 5) - 15 + 9
=|- 5 - 5| - (- 5 - 5) - 15 + 9
= |-10| - (-10) - 15 + 9
= 10 + 10 - 15 + 9
= 20 - 15+ 9
= 5 +9
= 14
Câu d:
- 20 - (25 - 11 + 8) +(25 - 8 + 20)
= - 20 - 25 + 11 - 8 + 25 - 8 + 20
= (-20 + 20) + (25 - 25) + (11 - 8- 8)
= 0 + 0+ 3 - 8
= -5
`Answer:`
a. \(\frac{17}{2}-\left|2x-\frac{3}{4}\right|=-\frac{7}{4}\)
\(\Leftrightarrow\left|2x-\frac{3}{4}\right|=\frac{17}{2}+\frac{7}{4}\)
\(\Leftrightarrow\left|2x-\frac{3}{4}\right|=\frac{41}{4}\)
\(\Leftrightarrow\orbr{\begin{cases}2x-\frac{3}{4}=\frac{41}{4}\\2x-\frac{3}{4}=-\frac{41}{4}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=\frac{41}{4}+\frac{3}{4}\\2x=-\frac{41}{4}+\frac{3}{4}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x=11\\2x=-\frac{19}{2}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=11:2\\x=-\frac{19}{2}:2\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{11}{2}\\x=-\frac{19}{4}\end{cases}}\)
b. \(\left(x+\frac{1}{5}\right)^2+\frac{17}{25}=\frac{26}{25}\)
\(\Leftrightarrow\left(x+\frac{1}{5}\right)^2=\frac{26}{25}-\frac{17}{25}\)
\(\Leftrightarrow\left(x+\frac{1}{5}\right)^2=\frac{9}{25}\)
\(\Leftrightarrow\left(x+\frac{1}{5}\right)=\left(\frac{3}{5}\right)^2\)
\(\Leftrightarrow\orbr{\begin{cases}x+\frac{1}{5}=\frac{3}{5}\\x+\frac{1}{5}=-\frac{3}{5}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{3}{5}-\frac{1}{5}\\x=-\frac{3}{5}-\frac{1}{5}\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{2}{5}\\x=-\frac{4}{5}\end{cases}}\)
c. \(-1\frac{5}{27}-\left(3x-\frac{7}{9}\right)^3=-\frac{24}{27}\)
\(\Leftrightarrow-\frac{32}{27}-\left(3x-\frac{7}{9}\right)^3=-\frac{24}{27}\)
\(\Leftrightarrow\left(3x-\frac{7}{9}\right)^3=-\frac{32}{27}-\left(-\frac{24}{27}\right)\)
\(\Leftrightarrow\left(3x-\frac{7}{9}\right)^3=-\frac{8}{27}\)
\(\Leftrightarrow\left(3x-\frac{7}{9}\right)^3=\left(-\frac{2}{3}\right)^3\)
\(\Leftrightarrow3x-\frac{7}{9}=-\frac{2}{3}\)
\(\Leftrightarrow3x=-\frac{2}{3}+\frac{7}{9}\)
\(\Leftrightarrow3x=\frac{1}{9}\)
\(\Leftrightarrow x=\frac{1}{9}:3\)
\(\Leftrightarrow x=\frac{1}{27}\)
Câu a:
- |- 5 + 3 - 7| - |- 5 + 7|
= -|- 2 - 7| - |2|
= - |-9| - 2
= - 9 - 2
= -11
Câu b:
24 - (72 - 13 + 24) - (72 - 13)
= 24 - 72 + 13 - 24 - 72 + 13
= (24 - 24) - (72 + 72) + (13 + 13)
= 0 - 144 + 26
= - 118
Câu c:
|4 - 9 - 5| - (4 - 9 - 5) - 15 + 9
=|- 5 - 5| - (- 5 - 5) - 15 + 9
= |-10| - (-10) - 15 + 9
= 10 + 10 - 15 + 9
= 20 - 15+ 9
= 5 +9
= 14
Câu d:
- 20 - (25 - 11 + 8) +(25 - 8 + 20)
= - 20 - 25 + 11 - 8 + 25 - 8 + 20
= (-20 + 20) + (25 - 25) + (11 - 8- 8)
= 0 + 0+ 3 - 8
= -5
Ta có: \(A=\dfrac{-5}{7}:\left(25-24\dfrac{4}{7}\right)+15\dfrac{1}{3}\cdot\dfrac{-1}{23}\)
\(=\dfrac{-5}{7}:\left(25-\dfrac{172}{7}\right)+\dfrac{46}{5}\cdot\dfrac{-1}{23}\)
\(=\dfrac{-5}{7}\cdot\dfrac{7}{3}+\dfrac{-2}{5}\)
\(=\dfrac{-5}{3}+\dfrac{-2}{5}\)
\(=\dfrac{-31}{15}\)