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1.53x201=10653
2.
a)4 xX-15x4=6x15+X
<=>4x-60=90+x
<=>4x-x=60+90
<=>3x=150
<=>x=50
b(102+28-2x):20-5=1
<=>(130-2x):20=6
<=>130-2x=120
<=>2x=10
<=>x=5
c)1999x-x=1999+1997+1999
<=>1998x=5995
<=>\(x\approx3\)
d)105-5x=150:15
<=>105-5x=10
<=>5x=95
<=>x=19
e)(x+1)+(x+2)+(x+3)+...+(x+6)=78
<=>6x+21=78
<=>6x=57
<=>x=9,5
1) 53x201=53x200+53=10600+53=10653
2a)
4x-15x4=6x15+x
4x-60=90+x
4x-x=90+60
3x=150
x=50
b) x=5
c) x=3
d)x=19
e) x=9,5
6 2/7 + 7 3/5 + 8 6/9 + 9 1/4 + 2/5 + 5/7 + 1/3 x 3/4 + 1967
= 44/7 + 38/5 + 78/9 + 37/4 + 2/5 + 5/7 + 1/3 + 1967
= ( 44/7 + 5/7 ) + ( 38/5 + 2/5 ) + ( 26/3 + 1/3 ) + ( 37/4 + 3/4 ) +1967
= 7 + 8 + 9 + 10 + 1967
= 15 + 9 + 10 + 1967
= 24 + 10 + 1967
= 34 + 1967
= 2001
b) \(\frac{3}{5}-\frac{1}{3}-\frac{1}{6}=\frac{18}{30}-\frac{10}{30}-\frac{5}{30}=\frac{8}{30}-\frac{5}{30}=\frac{1}{10}\)
c) \(\frac{4}{7}\times\frac{5}{8}\times\frac{7}{12}=\frac{4\times5\times7}{8\times12\times7}=\frac{5}{2\times12}=\frac{5}{24}\)
d) \(\frac{25}{28}:\frac{15}{14}\times\frac{6}{7}=\frac{25}{28}\times\frac{14}{15}\times\frac{6}{7}=\frac{25\times3}{15\times7}=\frac{75}{105}\)
\(\frac{7}{4}-x.\frac{3}{4}=\frac{5}{19}\)
\(\Rightarrow1+\frac{3}{4}-x.\frac{3}{4}=\frac{5}{9}\)
\(\Rightarrow\frac{3}{4}.\left(1-x\right)=\frac{5}{9}-1=-\frac{4}{9}\)
\(\Rightarrow1-x=-\frac{4}{9}:\frac{3}{4}=-\frac{16}{27}\)
\(\Rightarrow x=1-\left(-\frac{16}{27}\right)=1+\frac{16}{27}=1\frac{16}{27}\)
\(\frac{4}{7}.\frac{5}{36}.\frac{21}{25}\)
\(=\frac{4.5.21}{7.36.25}\)
\(=\frac{4.5.7.3}{7.4.9.5.5}\)
\(=\frac{3}{9.5}=\frac{3}{3.3.5}=\frac{1}{15}\)
\(\frac{25}{28}:\frac{15}{14}.\frac{6}{7}\)
\(=\frac{25.14.6}{28.15.7}\)
\(=\frac{5.5.14.6}{28.5.3.7}\)
\(=\frac{5.6}{2.3.7}=\frac{5.2.3}{2.3.7}\)
\(=\frac{5}{7}\)
\(\dfrac{2}{5}\times\dfrac{1}{7}+\dfrac{2}{7}\times\dfrac{2}{5}\)
\(=\dfrac{2}{5}\times\left(\dfrac{1}{7}+\dfrac{2}{7}\right)\)
\(=\dfrac{2}{5}\times\dfrac{3}{7}\)
\(=\dfrac{6}{35}\)
\(x+\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{3}{4}\)
\(x+\dfrac{1}{6}=\dfrac{3}{4}\)
\(x=\dfrac{9}{12}-\dfrac{2}{12}\)
\(x=\dfrac{7}{12}\)
\(\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times...\times\left(1-\dfrac{1}{2020}\right)+x=\dfrac{1}{2}\)
\(\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times...\times\dfrac{2019}{2020}+x=\dfrac{1}{2}\)
\(\dfrac{1}{2020}+x=\dfrac{1}{2}\)
\(x=\dfrac{1}{2}-\dfrac{1}{2020}\)
\(x=\dfrac{1010}{2020}-\dfrac{1}{2020}\)
\(x=\dfrac{1009}{2020}\)
\(\dfrac{2}{5}\times\dfrac{1}{7}+\dfrac{2}{7}\times\dfrac{2}{5}\)
\(=\dfrac{2}{5}\times\left(\dfrac{1}{7}+\dfrac{2}{7}\right)\)
\(=\dfrac{2}{5}\times\dfrac{3}{7}\)
\(=\dfrac{6}{35}\)
\(x+\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{3}{4}\)
\(\Rightarrow\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{3}{4}-x\)
\(\Rightarrow\dfrac{3}{4}-x=\dfrac{1}{6}\)
\(\Rightarrow x=\dfrac{3}{4}-\dfrac{1}{6}=\dfrac{7}{12}\)
\(\left(1-\dfrac{1}{2}\right)\times\left(1-\dfrac{1}{3}\right)\times\left(1-\dfrac{1}{4}\right)\times...\times\left(1-\dfrac{1}{2020}\right)+x=\dfrac{1}{2}\)
\(\Rightarrow\dfrac{1}{2}\times\dfrac{2}{3}\times\dfrac{3}{4}\times...\times\dfrac{2019}{2020}+x=\dfrac{1}{2}\)
\(\Rightarrow\dfrac{1\times2\times3\times4\times...\times2019}{2\times3\times4\times5\times...\times2020}+x=\dfrac{1}{2}\)
\(\Rightarrow\dfrac{1}{2020}+x=\dfrac{1}{2}\)
\(\Rightarrow x=\dfrac{1}{2}-\dfrac{1}{2020}=\dfrac{1009}{2020}\)
x=2
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