Expert: Scott A Wilson - 10/3/2011

Question
Im having trouble with these 5 problems.

Find the solution set of the inequality:
|   2   y   -   3   |   <   11

|   4   t   +   6   |    ≤   14

14   >   |   4   z   -   2   |

|   n   -   2   |   ≤   5

Solve the equation

|   7.5   -   5   n   |   =   2.5

PS: Its not part of a test or anything. Hope you can help.

Answer
Note that wheren there is an absolute value, it sets up two sets of two inequalities to solve
.
That is, for  |2y-3| < 11, we need 2y-3>0 and 2y-3<11  or  2y-3<0 and 3-2y<11.
For the 1st set, 2y-3<0 can have 3 added to both sides, so 2y>3.  Dividing by 2 gives y>3/2.  
For 2y-3<11, that is the same as 2y<14 => y<7.  Combining thes gives 3/2 < y < 7.
For the 2nd set, adding 3 to 2y-3<11 gives 2y<14.  Dividing by 2 gives y<7.

The others can be solved in a similar fashion.
| 4 t + 6 | ≤ 14  To solve this, solve (4t+6<14 and 4t+6>0) or (4t+6>14 and 4t-6<0).

Solve 14 < 4z-2 for 4z=2>0, so z
14 > | 4 z - 2 |

| n - 2 | ≤ 5

Solve the equation
| 7.5 - 5 n | = 2.5. Here, take 7.5-5n>0 and solve 7.5 - 5n = 2.5 or
7.5-5n<0  and solve -7.5 + 5n = 2.5.