Question

(b) Sketch the plane representing Ox + y + 4z = 4
(c) Solve:
[x - 12] = |4-x|
​

Answer 1

Given  : [x - 12] = |4-x|

​

To Find : Solve for x  

Solution :

[x - 12] = |4-x|

LHS has greatest integer function hence would always result in integer

and RHS can be integer only if x is integer

Hence x can have only integral values

so we can write it

x - 12   = | 4 - x |     as x - 12  is integer

Now | y |  = y  if y ≥ 0 and - y if y < 0

case 1     4 - x  ≥ 0   =>  x ≤  4

x - 12  = 4 - x

=> 2x  = 16

=> x = 8

but   x ≤  4  hence no possible solution

case 2     4 - x  <  0   =>  x > 4

x - 12  = -(4 - x)

=> x - 12  = x - 4

=>  -12 = - 4

which is incorrect

Hence no possible solution

There is no solution for   [x - 12] = |4-x|

However for  | x - 12 |  = | 4 - x |    x  =  8  is the solution

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Answer 2

Answer::

(b) Sketch the plane representing Ox + y + 4z = 4

(c) Solve:

[x - 12] = |4-x|