x-35/21 + x-36/20 > x-37/19 + x-38/18
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\(\frac{x+15}{35}+\frac{x+16}{36}=\frac{x+17}{37}+\frac{x+18}{38}\)
\(\frac{x+15}{35}-1+\frac{x+16}{36}-1=\frac{x+17}{37}-1+\frac{x+18}{38}-1\)
\(\frac{x-20}{35}+\frac{x-20}{36}-\frac{x-20}{37}-\frac{x-20}{38}=0\)
\(\left(x-20\right)\left(\frac{1}{35}+\frac{1}{36}-\frac{1}{37}-\frac{1}{38}\right)=0\)
\(\Rightarrow x-20=0\Rightarrow x=20\)
Vậy x=20
\(\frac{x+15}{35}+\frac{x+16}{36}=\frac{x+17}{37}+\frac{x+18}{38}\)
\(\Leftrightarrow\frac{x+15}{35}.885780+\frac{x+16}{36}.885780=\frac{x+17}{37}.885780+\frac{x+18}{38}.885780\)
\(\Leftrightarrow25308\left(x+15\right)+24605\left(x+16\right)=23940\left(x+17\right)+23310\left(x+18\right)\)
\(\Leftrightarrow49913x+773300=47250x+826560\)
\(\Leftrightarrow49913x=47250x+53260\)
\(\Leftrightarrow49913x-47250x=47250x+53260-47250x\)
\(\Leftrightarrow2663x=53260\)
\(\Leftrightarrow x=20\)
\(\Rightarrow x=20\)
18 x 38 + 16 x 76 -1 = ( 36 x 19 + 64 x 20 - 65 ) x X
( 36x 19 + 64 x 20 - 65 ) x X = 18x 38 + 16x 76 -1
1899 x X = 1899
X = 1899 / 1899
X = 1
18x38+16x76-1=[36x19+64x20-65]xX
[36x19+64x20-65]xX=18x38+16x76-1
1899xX=1899
x=1899/1899
x=1
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48+49+50=1275
c ) 815 - 23 - 77 + 185
= ( 815 + 185 ) - ( 23 + 77 )
= 1000 - 100 = 900
m ) 8 x 427 x 3 + 6 x 573 x 4
= 24 x 427 + 24 x 573
= 24 x ( 427 + 573 )
= 24 x 1000
= 24000
g ) 52 - 42 + 37 + 28 - 38 + 63
= ( 52 + 28 ) - ( 42 + 38 ) + ( 37 + 63 )
= 80 - 80 + 100
= 0 + 100
= 100
h ) 35 x 18 - 9 x 70 + 100
= 7 x 5 x 9 x 2 - 9 x 7 x 5 x 2 + 100
= 0 + 100
= 100
n ) 2008 x 867 + 2009 x 133
= 2008 x 867 + ( 2008 + 1 ) x 133
= 2008 x 867 + 2008 x 133 + 133
= 2008 x ( 867 + 133 ) + 133
= 2008 x 1000 + 133
= 2008000 + 133
= 2008133
i ) 326 x 78 + 327 x 22
= 326 x 78 + ( 326 + 1 ) x 22
= 326 x 78 + 326 x 22 + 22
= 326 x ( 78 + 22 ) + 22
= 326 x 100 + 22
= 32600 +22
= 32622
q ) ( 20 + 21 + 22 + 23 + 24 + 25 ) x ( 16 - 2 x 8 )
= ( 20 + 21 + 22 + 23 + 24 + 25 ) x ( 16 - 16)
= ( 20 + 21 + 22 + 23 + 24 + 25 ) x 0
= 0
a.245 x ( 327-18-9) = 245 x 300 = 73500
b. (462 - 62) x 4 = 1600
c. 900 : 9 = 100
d. (12+20) : 4 = 8
245x327-245x18-9x245 462 x 4 - 62 x 4
=245x(327-18-9) = ( 462 - 62) x 4
=245x300 = 400 x 4
=73500 = 1600
35 : 7 - 21 : 7 ( 25 x 36 ) : 9
= ( 35 - 21) : 7 = 900 : 9
= 14 : 7 = 100
= 2
12 : 4 + 20 : 4
= ( 12 + 20 ) : 4
= 32 : 4
= 8
Ta có : \(\frac{x-35}{21}+\frac{x-36}{20}>\frac{x-37}{19}+\frac{x-38}{18}\)(1)
\(\Leftrightarrow\left(\frac{x-35}{21}-1\right)+\left(\frac{x-36}{20}-1\right)\)\(-\left(\frac{x-37}{19}-1\right)-\left(\frac{x-38}{18}-1\right)\)\(>0\)
\(\Leftrightarrow\frac{x-56}{21}+\frac{x-56}{20}-\frac{x-56}{19}-\frac{x-56}{18}\)\(>0\)
\(\Leftrightarrow\left(x-56\right)\left(\frac{1}{21}+\frac{1}{20}-\frac{1}{19}-\frac{1}{18}\right)\)\(>0\)
Vì \(\frac{1}{21}+\frac{1}{20}-\frac{1}{19}-\frac{1}{18}< 0\)
\(\Rightarrow x-56< 0\)\(\Leftrightarrow x< 56\)
Vậy tập nghiệm của BPT(1) là \(S=\left\{x\in R|x< 56\right\}\)