Question

Rules for solving linear inequality problems plssss elaborate the topic fr better understanding

Answer 1

Here are some rules of solving linear inequalities
1)Adding or subtracting same number on both sides
2)Switching sides and changing the oeientation if the inequality sign.
3a)Multiplying or dividing by the same positive number on both sides.
3b)Multipying or dividing the same negative number on both sides and changing the orientation of the inequality sign.

Answer 2

It is simpler to show some rules by some examples...
The inequality symbols are :  <. >, <=  or ≤ , >= or ≥,  <> or  ≠  .

   2 x + 3 y ≤  25
   3 x - 2 y ≥ 5

  given,  a X +b Y <  c
1.   If you multiply with a positive number on LHS and RHS, then it is alright.  If you multiply with a negative number, then  the less than becomes greater than.

         - 2 a X - 2 b Y > - 2 c

2.  same rule for division too.
           -a/3  X  - b/3  Y  >  - c/3

3.  If you add or subtract  a term or number on both sides, then there is no problem.
                 a X + b Y  - d  <  c - d
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   we are given  two equations as:  2 x + 3 y ≤ 25
               and  3 x - 2y ≥  5

4. To  solve them,  convert both to have  either ≥  sign or  ≤ sign.
           2 x + 3 y ≤ 25
           2 y - 3 x ≤  - 5              multiplied by  -1 on both sides.

   multiply first equation by 3 and second by 2 and add both equations :
               13 y ≤ 65          =>   y ≤  5
 
Using the second equation now, with this value:
           3 x  ≥  2 y + 5
                 ≥  2 * 5 + 5  = 15
               x  ≥  5
 Now you can check for    y = 0,  1, 2 ,3,  4, 5  for example...

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5.  If      a  x   <  b  y          then        b y >  a x

6.       if  x  >  y  and  then    y > z,  we can say    x > z.

7.    if  x >  y    and      y < z,   then we cannot  say any thing about x and z.