解决以下方程式，并验证您的答案：
问题1.(2x-3)/(3x + 2)= -2/3
解决方案：
Given:
(2x-3) / (3x+2) = -2/3
After cross-multiplication we will get,
3(2x – 3) = -2(3x + 2)
6x – 9 = -6x – 4
Now rearrange the above equation
6x + 6x = 9 – 4
12x = 5
x = 5/12
Now verify the given equation by putting x = 5/12
(2x-3) / (3x+2) = -2/3
x = 5/12
(2(5/12) – 3) / (3(5/12) + 2) = -2/3
((5/6)-3) / ((5/4) + 2) = -2/3
((5-18)/6) / ((5+8)/4) = -2/3
(-13/6) / (13/4) = -2/3
(-13/6) × (4/13) = -2/3
-4/6 = -2/3
-2/3 = -2/3
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.
问题2.(2-y)/(y + 7)= 3/5
解决方案：
Given:
(2-y) / (y+7) = 3/5
After cross-multiplication we will get,
5(2-y) = 3(y+7)
10 – 5y = 3y + 21
Now rearrange the above equation,
10 – 21 = 3y + 5y
8y = – 11
y = -11/8
Now verify the given equation, by putting y = -11/8
(2-y) / (y+7) = 3/5
y = -11/8
(2 – (-11/8)) / ((-11/8) + 7) = 3/5
((16+11)/8) / ((-11+56)/8) = 3/5
(27/8) / (45/8) = 3/5
(27/8) × (8/45) = 3/5
27/45 = 3/5
3/5 = 3/5
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.
问题3.(5x – 7)/(3x)= 2
解决方案：
Given:
(5x – 7) / (3x) = 2
After cross-multiplication we will get,
5x – 7 = 2(3x)
5x – 7 = 6x
5x – 6x = 7
-x = 7
x = -7
Now verify the given equation but putting x = -7
(5x – 7) / (3x) = 2
x = -7
(5(-7) – 7) / (3(-7)) = 2
(-35 – 7) / -21 = 2
-42/-21 = 2
2 = 2
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.
问题4.(3x + 5)/(2x + 7)= 4
解决方案：
Given:
(3x+5) / (2x + 7) = 4
After cross-multiplication we will get,
3x + 5 = 4(2x+7)
3x + 5 = 8x + 28
3x – 8x = 28 – 5
-5x = 23
x = -23/5
Now verify the given equation by putting x =-23/5
(3x+5) / (2x + 7) = 4
x = -23/5
(3(-23/5) + 5) / (2(-23/5) + 7) = 4
(-69/5 + 5) / (-46/5 + 7) = 4
(-69+25)/5 / (-46+35)/5 = 4
-44/5 / -11/5 = 4
-44/5 × 5/-11 = 4
44/11 = 4
4 = 4
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.
问题5.(2y + 5)/(y + 4)= 1
解决方案：
Given:
(2y + 5) / (y + 4) = 1
After cross-multiplication we will get,
2y + 5 = y + 4
2y – y = 4 – 5
y = -1
Now verify the given equation by substituting y = -1
(2y + 5) / (y + 4) = 1
y = -1
(2(-1) + 5) / (-1 + 4) = 1
(-2+5) / 3 = 1
3/3 = 1
1 = 1
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.
问题6.(2x +1)/(3x – 2)= 5/9
解决方案：
Given:
(2x + 1) / (3x – 2) = 5/9
After cross-multiplication we will get,
9(2x + 1) = 5(3x – 2)
18x + 9 = 15x – 10
18x – 15x = -10 – 9
3x = -19
x = -19/3
Now verify the given equation byt substituting x = -19/3
(2x + 1) / (3x – 2) = 5/9
x = -19/3
(2(-19/3) + 1) / (3(-19/3) – 2) = 5/9
(-38/3 + 1) / (-57/3 – 2) = 5/9
(-38 + 3)/3 / (-57 – 6)/3 = 5/9
-35/3 / -63/3 = 5/9
-35/3 × 3/-63 = 5/9
-35/-63 = 5/9
5/9 = 5/9
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.
问题7.(1 – 9y)/(19 – 3y)= 5/8
解决方案：
Given:
(1 – 9y) / (19 – 3y) = 5/8
After cross-multiplication we willget,
8(1- 9y) = 5(19-3y)
8 – 72y = 95 – 15y
8 – 95 = 72y – 15y
57y = -87
y = -87/57
y = -29/19
Now verify the given equation by substituting y = -29/19
(1 – 9y) / (19 – 3y) = 5/8
y = -29/19
(1 – 9(-29/19)) / (19 – 3(-29/19)) = 5/8
(19+261)/19 / (361+87)/19 = 5/8
280/19 × 19/448 = 5/8
280/ 448 = 5/8
5/8 = 5/8
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.
问题8. 2x /(3x +1)= 1
解决方案：
Given:
2x / (3x + 1) = 1
After cross-multiplication we will get,
2x = 1(3x + 1)
2x = 3x + 1
2x – 3x = 1
-x = 1
x = -1
Now verify the given equation by substituting x = -1
2x / (3x + 1) = 1
x = -1
2(-1) / (3(-1) + 1) = 1
-2 /(-3+1) = 1
-2/-2 = 1
1 = 1
Here, L.H.S. = R.H.S.,
Thus the given equation is verified.
问题9. y –(7 – 8y)/ 9y –(3 + 4y)= 2/3
解决方案：
Given:
y – (7 – 8y)/9y – (3 + 4y) = 2/3
(y – 7 + 8y) / (9y – 3 – 4y) = 2/3
(-7 + 9y) / (5y – 3) = 2/3
After cross-multiplication we will get,
3(-7 + 9y) = 2(5y – 3)
-21 + 27y = 10y – 6
27y – 10y = 21 – 6
17y = 15
y = 15/17
Now verify the given equation by substituting y = 15/17
y – (7 – 8y)/9y – (3 + 4y) = 2/3
y = 15/17
15/17 – (7-8(15/17))/ 9(15/17) – (3 + 4(15/17)) = 2/3
15/17 – (7 – 120/17) / 135/17 – (3 + 60/17) = 2/3
15/17 – ((119-120)/17) / 135/17 – ((51+60)/17) = 2/3
15/17 – (-1/17) / 135/17 – (111/17) = 2/23
((15 + 1)/17) / ((135-111)/17) = 2/3
16/17 / 24/17 = 2/3
16/24 = 2/3
2/3 = 2/3
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.
问题10。6/ 2x –(3 – 4x)= 2/3
解决方案：
Given:
6/ 2x – (3 – 4x) = 2/3
6/(2x – 3 + 4x) = 2/3
6/(6x – 3) = 2/3
After cross-multiplication we will get,
3(6) = 2(6x – 3)
18 = 12x – 6
12x = 18 + 6
12x = 24
x = 24/12
x = 2
Now verify the given equation by substituting x = 2
6/ 2x – (3 – 4x) = 2/3
6/(6x – 3) = 2/3
x = 2
6/ (6(2) – 3) = 2/3
6/(12-3) = 2/3
6/9 = 2/3
2/3 = 2/3
Here, L.H.S. = R.H.S.,
Thus the given equation is verified.
问题11：2 / 3x – 3 / 2x = 1/12
解决方案：
Given:
2/3x – 3/2x = 1/12
By taking LCM for 2 and 3 which is 6
4-9/6x = 1/12
-5/6x = 1/12
After cross-multiplying we will get,
12(-5) = 1 (6x)
-60 = 6x
x = -60/6
x = -10
Now verify the given equation by substituting x = -10
2/3x – 3/2x = 1/12
x = -10
2/3(-10) – 3/2(-10) = 1/12
2/-30 – 3/-20 = 1/12
-4+6/60 = 1/12
5/60 = 1/12
1/12 = 1/12
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.
问题12(3x + 5)/(4x + 2)=(3x + 4)/(4x + 7)
解决方案：
Given:
(3x + 5)/ (4x + 2) = (3x + 4)/(4x + 7)
(3x + 5)/ (4x + 2) – (3x + 4)/(4x + 7) = 0
By taking LCM as (4x + 2) (4x + 7)
((3x + 5) (4x + 7) – (3x + 4) (4x + 2)) / (4x + 2) (4x + 7) = 0
After cross-multiplying we will get,
(3x + 5) (4x + 7) – (3x + 4) (4x + 2) = 0
(3x + 5) (4x + 7) – (3x + 4) (4x + 2) = 0
12x2 + 21x + 20x + 35 – 12x2 – 6x – 16x – 8 = 0
19x + 35 – 8 = 0
19x = -27
x = -27/19
Now verify the given equation by substituting, x = -27/19
(3x + 5)/ (4x + 2) = (3x + 4)/(4x + 7)
x = -27/19
(3(-27/19) +5) / (4(-27/19) + 2) = (3(-27/19) + 4) / (4(-27/19) + 7)
(-81/19 + 5) / (-108/19 + 2) = (-81/19 + 4) / (-108/19 + 7)
((-81+95)/19) / ((-108+38)/19) = ((-81+76)/19) / ((-108+133)/19)
14/19 / -70/19 = -5/19 / 25/19
-14/70 = -5/25
-1/5 = -1/5
Here, L.H.S. = R.H.S.,
Thus, the given equation is verified.