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a,
128-3x-12=23
3x=128-12-23
3x=93
x=93:3
= 31
b,
(12x+84+55):5=35
12x+84+55=35.5
12x+84+55=175
12x=175-55-84
12x=36
x=36:12
x=3
Bài toán 1 : Tìm x nguyên biết.
a. 3 ≤ x – 2 < 5
=>3-2 < x-2 < 5-2
=>1 < x < 3
=>x=1
Vậy x=1
b. 0 ≤ x – 5 ≤ 2
=>0-5 < x-5 < 2-5
=>-5 < x < -3
=>x=-4
Vậy x=-4
Bài toán 2 : Tính hợp lý.
a. 4567 + (1234 – 4567) -4
=4567+1234-4567-4
=(4567-4567)+(1234-4)
=0+1230
=1230
b. 2001 – (53 + 1579) – (-53)
=2001-53-1579+53
=(2001-1579)+(-53+53)
=422+0
=422
c. 35 – 17 + 2017 – 35 + (-2017)
=(35-35)+[2017+(-2017)]-17-35
=0+0-17-35
=0-17-35
=-52
d. 37 + (-17) – 37 + 77
=(37-37)+[-17+77]
=0+60
=60
e. –(-219) + (-219) – 401 + 12
=0-401+12
=-389
f. |-85| – (-3).15
=85+3.15
=85+45
=130
g. 11.107 + 11.18 – 25.11
=11.(107+18-25)
=11.100
=1100
h. 115 – (-85) + 53 – (-500 + 53)
=115+85+53+500-53
=(53-53)+(115+85+500)
=0+700
=700
k. (-18) + (-31) + 98 + |-18| + (-69)
=-18-31+98+18-69
=(-18+18)+(-31-69)+98
=0+(-100)+98
=-100+98
=-2
Bài toán 4 : Tìm x, biêt.
a. 5x – 16 = 40 + x
5x - x = 40 + 16
4x = 56
x = 56 : 4
x=14
b. 4x – 10 = 15 – x
4x + x = 15 + 10
5x = 25
x = 25 : 5
x = 5
c. -12 + x = 5x – 20
-12 + 20 = 5x - x
8 = 4x
x = 8 : 4
x = 2
d. 7x – 4 = 20 + 3x
7x - 3x = 20 + 4
4x=24
x=24:4
x=6
e. 5x – 7 = – 21 – 2x
5x + 2x = -21+7
7x = -14
x = -14 : 7
x = -2
f. x + 15 = 7 – 6x
x + 6x = 7 - 15
7x = -8
x = -8/7
g. 17 – x = 7 – 6x
17 - 7 = -6x + x
10 = -7x
x=10/-7
h. 3x + (-21) = 12 – 8x
3x + 8x = 12 + 21
11x = 33
x = 33:11
x=3
k. 125 : (3x – 13) = 25
3x-13=125:25
3x-13=5
3x=5+13
3x=18
x=18:3
x=6
l. 541 + (218 – x) = 735
218-x=735-541
218-x=693
x=218-693
x=-475
18 - 4\(x\) = -20 - 6\(x\)
-4\(x\) + 6\(x\) = - 20 - 18
2\(x\) = - 38
\(x\) = - 19
h, -15 \(\times\) 24 = -7\(x\) + 32
7\(x\) = 360 + 32
7\(x\) = 392
\(x\) = 392:7
\(x\) = 56
i, 15\(x\) -3.(4\(x\) - 6) = -12 + 36
15\(x\) - 12\(x\) + 18 = 24
3\(x\) = 24 - 18
3\(x\) = 6
\(x\) = 2
k, -10\(x\) - 27 = -7\(x\) + 33
-27 - 33 = -7\(x\) + 10\(x\)
3\(x\) = -60
\(x\) = -20
a) \(3x-10=2x+13\Leftrightarrow x=13+10=23\)
b) \(x+12=-5-x\Leftrightarrow2x=-17\Leftrightarrow x=-\frac{17}{2}\)
c) \(x+5=10-x\Leftrightarrow2x=5\Leftrightarrow x=\frac{5}{2}\)
d) \(6x+23=2x-12\Leftrightarrow4x=-35\Leftrightarrow x=-\frac{35}{4}\)
e) \(12-x=x+1\Leftrightarrow2x=11\Leftrightarrow x=\frac{11}{2}\)
f) \(14+4x=3x+20\Leftrightarrow x=20-14=6\)
g) \(2\left(x-1\right)+3\left(x-2\right)=x-4\Leftrightarrow2x-2+3x-6=x-4\)
\(\Leftrightarrow5x-8=x-4\Leftrightarrow4x=4\Leftrightarrow x=1\)
h ) \(3\left(4-x\right)-2\left(x-1\right)=x+20\Leftrightarrow12-3x-2x+2=x+20\)
\(\Leftrightarrow14-5x=x+20\Leftrightarrow6x=-6\Leftrightarrow x=-1\)
i ) \(4\left(2x+7\right)-3\left(3x-2\right)=24\Leftrightarrow8x+28-9x+6=24\)
\(\Leftrightarrow34-x=24\Leftrightarrow x=34-24=10\)
k) \(3\left(x-2\right)+2x=10\Leftrightarrow3x-6+2x=5x-6=10\)
\(\Leftrightarrow5x=10+6=16\Leftrightarrow x=\frac{16}{5}\)
Tự KL cho các phần
a) 5x - 16 = 40 + x
5x -x = 40 +16
4x = 56
x = 56 : 4
x = 14
b, 4x - 10 = 15 - x
4x + x = 15 +10
4x + x = 25
5x = 25
x = 25 : 5
x = 5
a) 128 - 3(x + 4) = 23
3(x + 4) = 128 -23
3(x + 4) = 105
x + 4 = 105 : 3
x + 4 = 35
x = 35 - 4
x = 31
\(a.128-3\left(x+4\right)=23.\)
\(3\left(x+4\right)=128-23\)
\(3\left(x+4\right)=105\)
\(x+4=105:3=35\)
\(x=35-4=31\)
\(b.\left[\left(4x+28\right)\cdot3+55\right]:5=35\)
\(\left(4x+28\right)\cdot3+55=35\cdot5=175\)
\(\left(4x+28\right)\cdot3=175-55=120\)
\(4x+28=120:3=40\)
\(4x=40-28=12\)
\(x=12:4=3\)
\(a.5\cdot\left(12-x\right)-20=30\\ 60-5x-20=30\\ 5x=10\\ x=2\\ b.\left(50-6x\right)\cdot18=8\cdot9\cdot5\\ 900-108x=360\\ 180x=540\\ x=3\\ c.128-3\cdot\left(x+4\right)=23\\ 128-3x-12=23\\ 3x=93\\ x=31\\ d.\left[\left(4x+28\right):3+55\right]:5=35\\ \left(4x+28\right):3=120\\ 4x+28=360\\ 4x=332\\ x=83\\ e.6x+4x=2010\\ x\cdot\left(6+4\right)=2010\\ 10x=2010\\ x=201\\ f.200-\left(2x+6\right)=64\\ 2x+6=136\\ 2x=130\\ x=65\)
\(g.135-5\cdot\left(x+4\right)=35\\ 5\cdot\left(x+4\right)=100\\x+4=20\\x=16\)
\(h.12x+13x=2000\\ x\cdot\left(12+13\right)=2000\\ x\cdot25=2000\\ x=80\\ i.\left(x-4\right)\cdot\left(x-3\right)=0\\ \Rightarrow x-4=0\Rightarrow x=4\\ x-3=0\Rightarrow x=3\\ \text{ vậy x = 4 hoặc x = 3 thì }\left(x-4\right)\cdot\left(x-3\right)=0\\ \)