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1)
a) 2x + 5 = 3⁴ : 3²
2x + 5 = 3²
2x + 5 = 9
2x = 9 - 5
2x = 4
x = 4 : 2
x = 2
b) (3x - 24).73 = 2.74
(3x - 24).73 = 148
3x - 24 = 148/73
3x = 148/73 + 24
3x = 1900/73
x = 1900/73 : 3
x = 1900/219
c) [3.(42 - x)] + 15 = 23.3
126 - 3x + 15 = 69
141 - 3x = 69
3x = 141 - 69
3x = 72
x = 72 : 3
x = 24
d) 126 + (132 - x) = 300
132 - x = 300 - 126
132 - x = 174
x = 132 - 174
x = -42
2)
a) 120 - (x + 55) = 60
x + 55 = 120 - 60
x + 155 = 60
x = 60 - 55
x = 5
b) (7x - 11).3 = 25.52 + 200
(7x - 11).3 = 1500
7x - 11 = 1500 : 3
7x - 11 = 500
7x = 500 + 11
7x = 511
x = 511 : 7
x = 73
c) 2x + 2x + 4 = 544
4x = 544 - 4
4x = 540
x = 540 : 4
x = 135
a: \(2^3-5^3:5^2+12\cdot2^2\)
\(=8-5+48\)
\(=51\)
b: \(5\cdot\left[\left(85-35:7\right):8+90\right]-5\)
\(=5\cdot\left[10+90\right]-5\)
=495
a, 2 3 x + 5 2 x = 2 5 2 + 2 3 - 33
8x+25x = 33
33x = 33
x = 1
b, 260 : x + 4 = 5 2 3 + 5 - 3 3 2 + 2 2
260:(x+4) = 5.13–3.13
x+4 = 260:26
x+4 = 10
x = 6
c, 720 : [ 41 - 2 x - 5 ] = 2 3 . 5
41–(2x–5) = 720:40
2x–5 = 41–18
2x = 28
x = 14
d, 3 2 - 2 x - 12 + 35 = 5 2 + 279 : 3 2
7(x–12)+35 = 56
7(x–12) = 21
x–12 = 3
x = 15
Bài làm
\(\frac{x+52}{21}+\frac{x+51}{22}=\frac{x+50}{23}+\frac{x+49}{24}\)
\(\Leftrightarrow\frac{x+52}{21}+\frac{x+51}{22}+2=\frac{x+50}{23}+\frac{x+49}{24}+2\)
\(\Leftrightarrow\left(\frac{x+52}{21}+1\right)+\left(\frac{x+51}{22}+1\right)=\left(\frac{x+50}{23}+1\right)+\left(\frac{x+49}{24}+1\right)\)
\(\Leftrightarrow\left(\frac{x+52}{21}+\frac{21}{21}\right)+\left(\frac{x+51}{22}+\frac{22}{22}\right)=\left(\frac{x+50}{23}+\frac{23}{23}\right)+\left(\frac{x+49}{24}+\frac{24}{24}\right)\)
\(\Leftrightarrow\frac{x+52+21}{21}+\frac{x+51+22}{22}=\frac{x+50+23}{23}+\frac{x+49+24}{24}\)
\(\Leftrightarrow\frac{x+73}{21}+\frac{x+73}{22}=\frac{x+73}{23}+\frac{x+73}{24}\)
\(\Leftrightarrow\frac{x+73}{21}+\frac{x+73}{22}-\frac{x+73}{23}-\frac{x+73}{24}=0\)
\(\Leftrightarrow\left(x+73\right)\left(\frac{1}{21}+\frac{1}{22}-\frac{1}{23}-\frac{1}{24}\right)=0\)
\(\Leftrightarrow x+73=0\)
\(\Leftrightarrow x=-73\)
Vậy x = -73
# Học tốt #
\(\frac{x+52}{21}+\frac{x+51}{22}=\frac{x+50}{23}+\frac{x+49}{24}\)
\(\Leftrightarrow\frac{x+52}{21}+\frac{x+51}{22}-\frac{x+50}{23}-\frac{x+49}{24}=0\)
\(\Leftrightarrow\left(\frac{x+52}{21}+1\right)+\left(\frac{x+51}{22}+1\right)-\left(\frac{x+50}{23}+1\right)-\left(\frac{x+49}{24}+1\right)=0\)
\(\Leftrightarrow\frac{x+73}{21}+\frac{x+73}{22}-\frac{x+73}{23}-\frac{x+73}{24}=0\)
\(\Leftrightarrow\left(x+73\right)\left(\frac{1}{21}+\frac{1}{22}-\frac{1}{23}-\frac{1}{24}\right)=0\)
=> \(x+73=0\left(\frac{1}{21}+\frac{1}{22}-\frac{1}{23}-\frac{1}{24}\ne0\right)\)
<=> x=-73
a: \(61\cdot45+61\cdot23-68\cdot51\)
\(=61\left(45+23\right)-68\cdot51\)
\(=68\cdot61-68\cdot51\)
\(=68\left(61-51\right)=68\cdot10=680\)
b: \(3\cdot5^2-\left(75-4\cdot2^3\right)\)
\(=75-75+4\cdot8\)
\(=4\cdot8=32\)
c: \(36:\left\{2^2\cdot5-\left[30-\left(5-1\right)^2\right]\right\}\)
\(=\dfrac{36}{20-30+4^2}\)
\(=\dfrac{36}{-10+16}=\dfrac{36}{6}=6\)
d: \(\left(12\cdot49-3\cdot2^2\cdot7^2\right):\left(2020\cdot2021\right)\)
\(=\dfrac{\left(12\cdot49-12\cdot49\right)}{2020\cdot2021}=0\)
22 x 43 - 625 : {[504 - (52 x 8 + 70) : 32 + 6] : 20 + 20230}
= 4 x 64 - 625 : {[504 - (25 x 8 + 70) : 9 + 6] : 20 + 1}
= 256 - 625 : {[504 - (200 + 70) : 9 + 6] : 20 + 1}
= 256 - 625 : {[504 - 270 : 9 + 6] : 20 + 1}
= 256 - 625 : {[504 - 30 + 6] : 20 + 1}
= 256 - 625 : {[474 + 6] : 20 + 1]
= 256 - 625 : {480 : 20 + 1]
= 256 - 625 : {24 + 1}
= 256 - 625 : 25
= 256 - 41
= 215
22 x 43 - 625 : {[504 - (52 x 8 + 70) : 32 + 6] : 20 + 20230}
= 4 x 64 - 625 : {[504 - (25 x 8 + 70) : 9 + 6] : 20 + 1}
= 256 - 625 : {[504 - (200 + 70) : 9 + 6] : 20 + 1}
= 256 - 625 : {[504 - 270 : 9 + 6] : 20 + 1}
= 256 - 625 : {[504 - 30 + 6] : 20 + 1}
= 256 - 625 : {[474 + 6] : 20 + 1]
= 256 - 625 : {480 : 20 + 1]
= 256 - 625 : {24 + 1}
= 256 - 625 : 25
= 256 - 41
= 215