I really need help on this one because I am really bad at graphing.
The problem goes like this: Solve and graph the solution set--
a) |4q - 18| > 0
This is one which you do not do any work on, you just reason it out
this way. Every absolute value of every number is always a number
which is NEVER negative, but always either ZERO or POSITIVE. But
that's exactly what "greater than or equal to ZERO" means. So
the solution set is "ALL REAL NUMBERS", which in interval notation is
(-oo, oo)
b) 12 - |7 - 2m| = 9
We add -12 to both sides
-|7 - 2m| = 9 - 12
-|7 - 2m| = -3
Multiply both sides by -1
|7 - 2m| = 3
To get rid of the absolute values,
break this into two separate
equations, and solve EACH:
7 - 2m = 3 OR 7 - 2m = -3
-2m = -4 OR -2m = -10
m = 2 OR m = 5
Those are the two solutions.
c) |r + 5| + 3 < 3
Subtract 3 from both sides
|r + 5| < 0
This is another one which you do not do like the others. You reason
it out this way. Every absolute value of every number is always a
number which is NEVER negative, but always either ZERO or POSITIVE. But
"less than or equal to ZERO" means "ZERO or negative". Since the
absiolute value |r + 5| can never be negative, then it can only be
ZERO, so
|r + 5| = 0
Or r + 5 = 0
r = -5
That is the only solution.
Edwin
