Question

Solve -
a) 2m - 3 = 3/10 (5m-12)
b) 6 (3a+2) - 5 (6a-1) = 3 (a-8) - 7 (5a-6) +9a
c) 9x+7/2 - (x-(x-2/7) ) = 36
d) 2 (m-2) - 3 (m-3) = 5 (m-5) - 4 (m-8)

Answer 1

a. 2m-3 = 3/10(5m-12)
    2m-3 = 15m-36/10
    10(2m-3) = 15m-36
    20m-30 = 15m-36
    20m - 15m = 30-36
    5m = -6
     m = -6/5

b.  6 (3a+2) - 5 (6a-1) = 3 (a-8) - 7 (5a-6) +9a
     18a+12-30a+5 = 3a-24-35a+42+9a
      -12a+17 = -23a+18
      23a-12a = 18-17
      11a = 1
       a = 1/11

c. 9x+7/2 - (x-(x-2/7) ) = 36
    [9x(2)+7] / 2 - (x-([7x-2/7)) = 36
    [18x+7] / 2 -  (x-7x+2/7) = 36
    [18x+7] / 2 -  (-6x+2/7) = 36
    lcm of 2, 7 is 14
    [18x(7) +7(7) +6x(2)-2(2)] / 7 = 36
    126x+44+12x-4/7 = 36
    138x+40=36×7
    138x = 252 - 40
     138x = 212
     x = 106/69

d. 2 (m-2) - 3 (m-3) = 5 (m-5) - 4 (m-8)
    2m-4-3m+9 = 5m-25-4m+32
    5-m = m + 7
     m+m = 5-7
    2m = -2
    m = -1
    
   
    

Answer 2

$2m-3=\frac{3}{10}(5m -12)\\\\10*(2m-3)=3*(5m-12)\\\\20 m - 30 = 15 m - 36\\\\5m =-6\\\\m=-\frac{6}{5}$
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6 (3 a + 2)  -  5 (6 a - 1) =  3 ( a  - 8) - 7 ( 5 a - 6) + 9 a
18 a + 12  - 30 a + 5 = 3 a - 24 - 35 a + 42 + 9 a
- 12 a + 17 = - 23 a + 18
23 a - 12 a = 18 - 17
11 a = 1
a =  1 / 11

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here it is not clear  if the  2 in denominator, has numerator  7  or  9 x + 7 ??
           same way,  it is x-2  or  2 in the numerator for  denominator 7 ?

case 1:

$9 x + \frac{7}{2} - (x - (x -\frac{2}{7})) = 36\\\\9 x + \frac{7}{2}-( x - x +\frac{2}{7}) = 36\\\\9 x + \frac{7}{2} -\frac{2}{7} = 36\\\\9 x + \frac{7*7 - 2*2}{14}= 36\\\\9 x + \frac{45}{14} = 36,\ \ \ \ divide\ by\ 9\\\\x = 4- \frac{5}{14}\\\\x =\frac{56- 5}{14}\\\\x = \frac{51}{14}$
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case 2:

$\frac{9 x+7}{2} - ( x - \frac{x - 2}{7})\\\\=\frac{9 x+7}{2} - (\frac{7x-x + 2}{7})\\\\=\frac{9 x+7}{2} - (\frac{6x + 2}{7})\\\\=\frac{7(9x+7)-2(6x+2)}{2*7}\\\\=\frac{63x+49-12x-4}{14}\\\\=\frac{51x+45}{14}\\\\=\frac{3(17x+15)}{14}$