We solve the given equations as per steps described below.

1)

9 - (x + 4) = 12 + 7(2x - 3)

9 - x - 4 = 12 + 14x - 21

Transferring all terms with x on left hand side and all terms with only numbers on right hand side of the equation:

- x - 14x = 12 - 21 - 9 + 4

-15x = - 14

Therefore:

x = (-14)/(-15) = 14/15

2)

6x - (4x - 13) + 3 = 5- (x-3)

6x - 4x + 13 + 3 = 5 - x + 3

Transferring all terms with x on left hand side and all terms with only numbers on right hand side of the equation:

6x - 4x + x = 5 + 3 - 13 - 3

3x = - 8

Therefore:

x = -8/3

1)For solving the linear equation 9-(x+4)=12+7(2x-3), we'll have to open the parantheses first.

9-x-4=12+14x-21

Now, we'll move all terms which contain the unknown, to the left side, and all terms without x, to the right side, changing their signs of the terms which have been moved:

-x-14x = -9+4+12-21

-15x = -14

**x = 14/15**

2) We'll do the same way as above.

6x-4x+13+3 = 5-x+3

2x+x=-16+8

3x=-8

**x=-8/3**

To solve:

1) 9-(x+4)=12+7(2x-3)

Solution:

This is a linear eqution in one variable x. We open the bracket on both sides and by simple operations of (i)adding (suitable) equals to both sides Or (ii) subtracting suitable equals from both sides or (iii) multiplying by suitable equals both sides or (iv) diving by suitable equals (but never dividing by zeros) both sides we move allx's to one side and numbers to the other side and come to a come to the result x = a number which is the solution.

9-(x+4)=12+7(2x-3). Or

9-x-4 =12+7*2x-7*3 Simplify by collecting likestogether on both sides:

5 -x = 14x- 9 . Subtract 14x from both sides:

5-x-14x=14x-9 -14x. Simplify:

5-15x=-9. Subract -5 from both sides:

5-15x - 5 = -9-5. Simplify:

-15x = - 14. Divide both sides by -15;

-15x/(-15) = -14/(-15) = 14/15

2) To solve 6x-(4x-13)+3=5-(x-3)

We follow the steps said in the above solution by opening the brackets following the rules of sign.

6x-4x-(-13)+3=5-x-(-3). Or

2x+13+3 =5-x+3 . Or

2x+16=8-x. Add x to both sides:

3x+16 = 8. Subtract 16 from both sides:

3x = 8-16 =-8. Divide by 3 both sides:

x = -8/3

Check: Substite the solution x =-8/3 in the given equation and see if you get equal values on left side and right side. If you get not equal values, then the solution is wrong . Again you have to check all the calculation. If you get equal values then **most probably** we are right (why?).