a) x=53

b) x=17

c) x=5;x=-5

d) x=17

e) x=5

g) ???

......

đáp số:?

\(\frac{4}{3}.\left(\frac{1}{6}-\frac{1}{2}\right)< x< \frac{2}{3}.\left(\frac{-1}{6}+\frac{3}{4}\right)\)

⇒ \(\frac{4}{3}.\left(\frac{-1}{3}\right)< x< \frac{2}{3}.\left(\frac{7}{12}\right)\)

⇒ \(\frac{-4}{9}< x< \frac{7}{18}\)

⇒ \(\frac{-8}{18}< x< \frac{7}{18}\)

mà -8<x<7

⇒ x ϵ \(\left\{-7;-6;-5;-4;....;5;6\right\}\)

a, 5x=-36+16=20

=>x=4

b, 4x=10-(-2)=12

=>x=3

c, x-5=-10 : 2= -5

=> x=0

d, 40+x=-80

=> x=-80-40=-120

e, 15-x=-40

=> x=15-(-40)=55

f, x=6+15+4x=21+4x

=>x-4x=21

=>-3x=21

=> x = -7

a) \(\left(\dfrac{1}{2}x-3\right)\left(-\dfrac{1}{3}+x\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x-3=0\\-\dfrac{1}{3}+x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{2}x=0+3\\-\dfrac{1}{3}+x=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=3:\dfrac{1}{2}\\x=0-\left(-\dfrac{1}{3}\right)\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=\dfrac{1}{3}\end{matrix}\right.\)

d) \(9x^2=1\)

\(\Leftrightarrow x^2=1:9\)

\(\Leftrightarrow x^2=\dfrac{1}{9}\)

\(\Leftrightarrow x^2=\left(\dfrac{1}{3}\right)^2\)

\(\Leftrightarrow x=\dfrac{1}{3}\)

a) 2.3^x =162

3^x =162:2

3^x=81

3^x=3⁴

vậy x bằng 4

ban co the lam cau b) , c) khong

\(a,\)\(-\frac{3}{5}\cdot x=\frac{1}{4}+0,75\)

\(-\frac{3}{5}\cdot x=\frac{1}{4}+\frac{3}{4}=\frac{4}{4}=1\)

\(x=1\div\left(-\frac{3}{5}\right)\)

\(x=-\frac{5}{3}\)

\(b,\)\(\left(\frac{1}{7}-\frac{1}{3}\right)\cdot x=\frac{28}{5}\times\left(\frac{1}{4}-\frac{1}{7}\right)\)

\(\left(\frac{3}{21}-\frac{7}{21}\right)\cdot x=\frac{28}{5}\cdot\left(\frac{7}{28}-\frac{4}{28}\right)\)

\(-\frac{4}{21}\cdot x=\frac{28}{5}\cdot\frac{3}{28}\)

\(-\frac{4}{21}\cdot x=\frac{3}{5}\)

\(x=\frac{3}{5}\div\left(-\frac{4}{21}\right)\)

\(x=-\frac{63}{20}\)

\(c,\)\(\frac{5}{7}\cdot x=\frac{9}{8}-0,125\)

\(\frac{5}{7}\cdot x=\frac{9}{8}-\frac{1}{8}\)

\(\frac{5}{7}\cdot x=1\)

\(x=1\div\frac{5}{7}\)

\(x=\frac{7}{5}\)

\(d,\)\(\left(\frac{2}{11}+\frac{1}{3}\right)\cdot x=\left(\frac{1}{7}-\frac{1}{8}\right)\cdot36\)

\(\left(\frac{6}{33}+\frac{11}{33}\right)\cdot x=\left(\frac{8}{56}-\frac{7}{56}\right)\cdot36\)

\(\frac{17}{33}\cdot x=\frac{1}{56}\cdot36\)

\(\frac{17}{33}\cdot x=\frac{9}{14}\)

\(x=\frac{9}{14}\div\frac{17}{33}\)

\(x=\frac{9}{14}\cdot\frac{33}{17}=\frac{297}{238}\)

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left[x+1\right]}=\frac{2007}{2009}\)

\(\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+...+\frac{2}{x\left[x+1\right]}=\frac{2007}{2009}\)

\(2\left[\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{x\left[x+1\right]}\right]=\frac{2007}{2009}\)

\(2\left[\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right]=\frac{2007}{2009}\)

\(2\left[\frac{1}{2}-\frac{1}{x+1}\right]=\frac{2007}{2009}\)

\(1-\frac{2}{x+1}=\frac{2007}{2009}\)

\(\frac{2}{x+1}=1-\frac{2007}{2009}\)

\(\frac{2}{x+1}=\frac{2}{2009}\)

\(\Rightarrow x+1=2009\Leftrightarrow x=2008\)