a) 156-(x+61)=82 b) (x-35)-120=0 c) 124-(x-118)=217 d) 2x-49=5.3^2 e) 200-(2x+6)=4^3 f) 2(x-51)=2.2^3+20 g) 4(x-3)=7^2-1^10 h) 3^2(x+4)-5^2=5.2^2 i) 9^x-1=9
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a) \(5x-65=5.3^2 \\ 5x-65=45\\5x=45+65\\5x=110\\x=22\)
b) \(200-(2x+6)=4^3\\2x+6=200-4^3\\2x+6=136\\2x=130\\x=65\)
c) \(2(x-51)=2.2^3+20\\2(x-51)=16+20\\2(x-51)=36\\x-51=18\\x=51+18=69\)
d) \(135-5(x+4)=35\\5(x+4)=135-45\\5(x-4)=90\\x-4=18\\x=18+4=22\)
e) \((2x-4)(15-3x)=0\\2(x-2).3(5-x)=0\\(x-2)(5-x)=0\\ \left[ \begin{array}{l}x-2=0\\5-x=0\end{array} \right. \\ \left[ \begin{array}{l}x=2\\x=5\end{array} \right.\)
f) \(2^{x+1} . 2^{2014}=2^{2016} \\ (2^{x+1} . 2^{2014}):2^{2014}=2^{2016} :2^{2014} \\ 2^{x=1}=2^{2016-2014} \\2^{x+1}=2^2\\x+1=2\\x=1\)
g) \(15+(x-1)^3=43\\(x-1)^3=15-42\\(x-1)^3=-27\\(x-1)^3=(-3)^3\\x-1=-3\\x=-2\)
h) \(15-x=17+(-9)\\15-x=17-9\\15-x=8\\x=15-8\\x=7\)
i) \(|x-5|=|-7|+|-4|\\|x-5|=7+4\\|x-5|=11\\ \left[ \begin{array}{l}x-5=11\\x-5=-11\end{array} \right. \\ \left[ \begin{array}{l}x=16\\x=-6\end{array} \right.\)
k) \(|x-3|-12=-9+|-7|\\|x-3|-12=-9+7\\|x-3|-12=-2\\|x-3|=10 \\ \left[ \begin{array}{l}x-3=10\\x-3=-10\end{array} \right. \\ \left[ \begin{array}{l}x=13\\x=-7\end{array} \right.\)
a) 2(x-51) = 2^0.2^4 + 5.2^2
2(x-51) = 2^2(2^2+5)
2(x-51) = 36
x-51 = 18
x = 69
Vậy: x = 69
b) 225 : (x-19) = 25
x-19 = 9
x = 28
Vậy: x = 28
c) 4. (x-3)= 7^2-1^0
4. (x-3)= 48
x-3 = 12
x = 15
Vậy: x = 15
d) 3^3(x+4) - 3.5^2= 15.2^2
27 (x+4) - 75 = 60
27 (x+4) = 135
x+4 = 5
x = 1
Vậy: x = 1
e) 2x-7^2 = 5.3^2
2x - 49 = 45
2x = 94
x = 47
Vậy: x = 47
f) 2^3.5^2-(2x+6) = 4^3
200 - 2x - 6 = 64
194 - 2x = 64
2x = 130
x = 65
Vậy: x = 65
g) 135 - 5(x+4) = 35
5(x+4) = 100
x + 4 = 20
x = 16
Vậy: x = 16
h) 75 + 9(x-8) = 318
9(x-8) = 243
x-8 = 27
x = 35
Vậy: x = 35
1) (x - 35) - 120 = 0
x - 35 = 120
x = 120 + 35
x = 155
2) 310 - (118 - x) = 217
118 - x = 310 - 217
118 - x = 93
x = 118 - 93
x = 25
3) 156 - (x + 61) = 82
x + 61 = 156 - 82
x + 61 = 74
x = 74 - 61
x = 13
4) 814 - (x - 305) = 712
x - 305 = 814 - 712
x - 305 = 102
x = 102 + 305 = 407
5) 100 - 7 - (x - 5) = 58
x - 5 = 93 - 58
x - 5 = 35
x = 35 + 5 = 40
6) 12(x - 1) : 3 = 43 + 23
4(x - 1) = 72
x - 1 = 18
x = 18 + 1 = 19
7) 24 + 5x = 75 : 73
24 + 5x = 49
5x = 25
x = 25 : 5 = 5
8) 5(x - 1) : 3 = 43 + 23
\(\dfrac{5}{3}\left(x-1\right)=72\)
x - 1 = \(\dfrac{216}{5}\)
x = 221/5
9) 5(x - 4)2 - 7 = 13
5(x - 4)2 = 20
(x - 4)2 = 4
\(\Rightarrow\left[{}\begin{matrix}x-4=2\\x-4=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=6\\x=2\end{matrix}\right.\)
10) (x + 1) + (x + 2) + ... + (x + 30) = 795
=> (x + x + x + ... + x) + (1 + 2 + 3 +...+ 30) = 795 (1)
Đặt A = 1 + 2 + 3 +...+ 30
Số số hạng trong A là: (30 - 1) : 1 + 1 = 30 (số)
Tổng A bằng : (30 + 1).30 : 2 =465
Thay A = 465 vào (1) , ta được:
30x + 465 = 795
=> 30x =330
=> x =11
1: =>x-35=120
=>x=120+35=155
2: =>118-x=310-217=93
=>x=118-93=25
3: =>x+61=156-82=74
=>x=74-61=13
4: =>x-305=814-712=102
=>x=102+305=407
5: =>93-(x-5)=58
=>x-5=35
=>x=40
6: =>4(x-1)=64+8=72
=>x-1=18
=>x=19
7: =>5x+24=49
=>5x=25
=>x=5
8: =>5(x-1):3=4^3+2^3=64+8=72
=>5(x-1)=216
=>x-1=216/5
=>x=221/5
a) 89-(73-x) = 20
=> 73+x =89-20
=> 73+x=69
=> x=69-73
=> x=-4
b) (x+7)-25=13
=> x+7=13+25
=> x+7=38
=> x=38-7
=> x=31
c) 98-(x+4)=20
=> x+4=98-20
=> x+4=78
=> x=78-4
=> x=73
d) 140:(x-8)=7
=> x-8=140:7
=> x-8=20
=> x=20+8
=> x=28
e) 4(x+41)=400
=> x+41=400:4
=> x+41=100
=> x=100-41
=> x=59
f) x-[42+(-28)]=-8
=> x-14=-8
=> x=-8+14
=> x=6
`a,4x-10=0 `
`<=> 4x=10`
`<=>x=10/4`
`<=>x=5/2`
`b, 7-3x=9-x `
`<=>-3x+x=9-7`
`<=>-2x=2`
`<=>x=-1`
`c, 2x-(3-5x) = 4(x+3)`
`<=>2x-3+5x=4x+12`
`<=>2x+5x-4x=12+3`
`<=>3x=15`
`<=>x=5`
`d, 5-(6-x)=4(3-2x) `
`<=>5-6+x=12-8x`
`<=>x+8x=12-5+6`
`<=>9x=13`
`<=>x=13/9`
`e, 4(x+3)=-7x+17 `
`<=>4x+12=-7x+17`
`<=>4x+7x=17-12`
`<=>11x=5`
`<=>x=5/11`
`f, 5(x-3) - 4=2(x-1)+7`
`<=>5x-15-4=2x-2+7`
`<=>5x-2x=15+4-2+7`
`<=>3x=24`
`<=>x=8`
`g, 5(x-3)-4=2(x-1)+7 `
`<=>5x-15-4=2x-2+7`
`<=>5x-2x=15+4-2+7`
`<=>3x=24`
`<=>x=8`
`h,4(3x-2)-3(x-4)=7x+20`
`<=>12x-8-3x+12=7x+20`
`<=>12x-3x-7x=20+8+12`
`<=>2x=40`
`<=>x=20`
a) 124 + (118 - x) = 217
118 - x = 217 - 124
118 - x = 93
x = 118 - 93
x = 25
b) 156 - (x + 61) = 82
x + 61 = 156 - 82
x + 61 = 74
x = 74 - 61
x = 13
c) 219 - 7(x + 1) = 100
7(x + 1) = 219 - 100
7(x + 1) = 119
x + 1 = 119 : 7
x + 1 = 17
x = 17 - 1
x = 16
d) (3x - 6).3 = 3⁴
3x - 6 = 3⁴ : 3
3x - 6 = 3³
3x - 6 = 27
3x = 27 + 6
3x = 33
x = 33 : 3
x = 11
e) 231 - (x - 6) = 1339 : 13
231 - (x - 6) = 103
x - 6 = 231 - 103
x - 6 = 128
x = 128 + 6
x = 134
a) 124 + (118 - x) = 217
118 - x = 217 - 124
118 - x = 93
x = 118 - 93
x = 25
b) 156 - (x + 61) = 82
x + 61 = 156 - 82
x + 61 = 74
x = 74 - 61
x = 13
c) 219 - 7(x + 1) = 100
7(x + 1) = 219 - 100
7(x + 1) = 119
x + 1 = 119 : 7
x + 1 = 17
x = 17 - 1
x = 16
d) (3x - 6) . 3 = 34
(3x - 6) . 3 = 81
(3x - 6) = 81 : 3
(3x - 6) = 27
3x = 27 + 6
3x = 33
x = 33 : 3
x = 11
e) 231 - (x - 6) = 1339 : 13
231 - (x - 6) = 103
(x - 6) = 231 - 103
x - 6 = 128
x = 128 + 6
x = 134
a) 71 - (33 + x) = 26
⇔ 71 - 33 - x = 26
⇔ 38 - x = 26
⇔ x = 38 - 26
⇔ x = 12
b) (x + 73) - 26 = 76
⇔ x + 73 - 26 = 76
⇔ x + 47 = 76
⇔ x = 76 - 47
⇔ x = 29
c) 45 - (x + 9) = 6
⇔ 45 - x - 9 = 6
⇔ 36 - x = 6
⇔ x = 36 - 6
⇔ x = 30
d) 89 - (73 - x) = 20
⇔ 89 - 73 + x = 20
⇔ 16 + x = 20
⇔ x = 20 - 16
⇔ x = 4
e) (x + 7) - 25 = 13
⇔ x + 7 - 25 = 13
⇔ x - 18 = 13
⇔ x = 13 + 18
⇔ x = 31
f) 198 - (x + 4) = 120
⇔ 198 - x - 4 = 120
⇔ 194 - x = 120
⇔ x = 194 - 120
⇔ x = 74
g) 140 : (x - 8) = 7
⇔ x - 8 = 140 : 7
⇔ x - 8 = 20
⇔ x = 20 + 8
⇔ x = 28
h) 4(x + 41) = 400
⇔ x + 41 = 400 : 4
⇔ x + 41 = 100
⇔ x = 100 - 41
⇔ x = 59
i) 11(x - 9) = 77
⇔ x - 9 = 77 : 11
⇔ x - 9 = 7
⇔ x = 7 + 9
⇔ x = 16
j) 5(x - 9) = 350
⇔ x - 9 = 350 : 5
⇔ x - 9 = 70
⇔ x = 70 + 9
⇔ x = 79
k) 2x - 49 = 5.32
⇔ 2x - 49 = 45
⇔ 2x = 45 + 49
⇔ 2x = 94
⇔ x = 94 : 2
⇔ x = 47
l) 200 - (2x + 6) = 43
⇔ 200 - 2x - 6 = 64
⇔ 194 - 2x = 64
⇔ 2x = 194 - 64
⇔ 2x = 130
⇔ x = 130 : 2
⇔ x = 65
a) 71 - (33 + x) = 26
⇔ 33+x=71-26
⇔ 33 + x = 45
⇔ x = 45 - 33
⇔ x = 12
Vậy x=12
b) (x + 73) - 26 = 76
⇔ (x + 73) = 76+26
⇔ x + 73 = 102
⇔ x = 102-73
⇔ x = 29
Vậy x=29
c) 45 - (x + 9) = 6
⇔ x + 9 = 45 - 6
⇔ x+9 = 39
⇔ x = 39 - 9
⇔ x = 30
Vậy x=30