Bài 5
a) 1/3 : (x - 1/2) + 5/6 = -3/2
1/3 : (x - 1/2) = -3/2 - 5/6
1/3 : (x - 1/2) = 7/3
x - 1/2 = 1/3 : 7/3
x - 1/2 = 1/7
x = 1/7 + 1/2
x = 3/14
b) (0,16 + 0,01)²x = 0,9
(0,4 + 0,1)²x = 0,9
0,5².x = 0,9
0,25.x = 0,9
x = 0,9 : 0,25
x = 3,6
c) x + (-3/4) : 1 1/8 = 1/3
x - 3/4 : 9/8 = 1/3
x - 2/3 = 1/3
x = 1/3 + 2/3
x = 1
d) (2x - 1)⁴ = 81
(2x - 1)⁴ = 3⁴
2x - 1 = 3 hoặc 2x - 1 = -3
*) 2x - 1 = 3
2x = 4
x = 4 : 2
x = 2
*) 2x - 1 = -3
2x = -2
x = -2 : 2
x = -1
Vậy x = -1; x = 2
Bài 4
a) -1/10 + 2/5 x + 7/20 = 1/10
2/5 x = 1/10 + 1/10 - 7/20
2/5 x = -3/20
x = -3/20 : 2/5
x = -3/8
b) 1/3 + 1/2 : x = -1/5
1/2 : x = -1/5 - 1/3
1/2 : x = -2/15
x = 1/2 : (-2/15)
x = -15/4
c) -2/3 : x + 5/8 = -7/12
-2/3 : x = -7/12 - 5/8
-2/3 : x = -33/8
x = -2/3 : (-33/8)
x = 16/99
d) 1/2 x + 2 1/2 = 3 1/2 x - 3/4
1/2 x + 5/2 = 7/2 x - 3/4
7/2 x - 1/2 x = 5/2 + 3/4
3x = 13/4
x = 13/4 : 3
x = 13/12
Bài 4
e) 2/3 x - 2/5 = 1/2 x - 1/3
2/3 x - 1/2 x = -1/3 + 2/5
1/6 x = 1/15
x = 1/15 : 1/6
x = 2/5
f) 1/3 x + 2/5 (x + 1) = 0
1/3 x + 2/5 x + 2/5 = 0
11/15 x = -2/5
x = -2/5 : 11/15
x = -6/11
g) 2/3 - 1/3 (x - 3/2) - 1/2 (2x + 1) = 5
2/3 - 1/3 x + 1/2 - x - 1/2 = 5
-4/3 x = 5 - 2/3
-4/3 x = 13/3
x = 13/3 : (-4/3)
x = -13/4
h) (x + 2015)/5 + (x + 2016)/4 = (x + 2017)/3 + (x + 2018)/2
(x + 2015)/5 + 1 + (x + 2016)/4 + 1 = (x + 2017)/3 + 1 + (x + 2018)/2 + 1
(x + 2020)/5 + (x + 2020)/4 = (x + 2020)/3 + (x + 2020)/2
(x + 2020)/5 + (x + 2020)/4 - (x + 2020)/3 - (x + 2020)/2 = 0
(x + 2020).(1/5 + 1/4 - 1/3 - 1/2) = 0
x + 2020 = 0
x = -2020
i) |x + 4/5| - 1/7 = 0
|x + 4/5| = 1/7
x + 4/5 = 1/7 và x + 4/5 = -1/7
*) Với x ≥ -4/5, ta có:
x + 4/5 = 1/7
x = 1/7 - 4/5
x = -23/35 (nhận)
*) Với x < -4/5, ta có:
x + 4/5 = -1/7
x = -1/7 - 4/5
x = -33/35 (nhận)