Question 63036

 given 0 < 5 - 2x < = 10

consider the first part  0 < 5 - 2x

==>         0 + 2x < 5 - 2x + 2x  [adding 2x to both the sides of the equation]
==>          2x < 5
==>       2x/2 < 5/2
==> x < 5/2  --------------------(1)

Consider the second part 5 - 2x <= 10
==>       5 - 2x - 5 <= 10 - 5
==>        - 2x <= 5
==>         2x >= -5 [once we changwe the sign, the inequality changes]
==>        2x/2 >= -5/2
==>         x >= - 5/2  ------------------(2)

Combining (1) andd (2) the solution in interval notation would be [-5/2, 5/2)



(2)  -6 < 4-x < 0

 Consider the first part of the inequality -6 < 4-x
==>                                   -6 - 4 < 4 - x - 4
==>                                  - 10 < -x
==>                                    10 > x ---------------(1)

the second part, 4 - x < 0
==>               4 - x - 4 < 0 - 4
==>                  -x < - 4
==>                   x > 4 ------------------------(2)


Combining (1) andd (2) the solution in interval notation would be (4, 10)



Good Luck!!!