Absolute value frequently misunderstood

1
Algebra II/Trig 1.7
Block 1-4
Absolute value (frequently misunderstood!!!)
Distance from zero!!! Simplify -5
-5 -3 7 -3 7 Solve an
equation x 3 . . . . . think . . . where are
you on the number line when you are 3 units from
zero? x 3 or x -3 Rules for solving an
absolute value equation 1. ISOLATE the absolute
value term 2. Use the definition to write TWO
equations 3. Check your work.
x 3 -5
x 4
2x 5 - 2 -1
3x - 1 x 1
You can use the graphing calculator to check your
answers!!! Put the left side of the equation
into y1 and put the right side into y2. Use the
graph or the table to find the point(s) of
intersection. (Absolute value symbols are under
the math button).
2
Absolute value inequalities just require a little
more thought. x lt 3 If x is always
less than three units from zero, show where it
can be x lt 3 means -3 lt x lt 3 x
gt 3 If x is always more than three units
from zero, show where it can be
x gt 3 means x lt - 3 or x gt 3
Your mission (you have no choice . . . you must
accept it!!!)
Memorize these relationships x lt 3 means
-3 lt x lt 3 Less thAN(D)
x gt 3 means x lt - 3 or
x gt 3 GreatOR
See this problem 2x 3 gt 5 Use the greatOR
relationship 2x 3 lt - 5 or 2x 3
gt 5
See this problem 2x 3 5 Use
the less than(D) relationship -5 2x 3
5
Special cases x gt -3 Since absolute value is
always positive and positive numbers are always
greater than negatives, the solution set is ALL
REALS. x lt -3 Same theory as above NO
SOLUTIONS!!! Write the absolute value
inequalities that would correspond with these
graphs
HW page 45 43 - 51 odd page 55 start with
9 and work DOWN the first column page 56 start
with 40 and work DOWN the first column until you
finish 65 page 57 74, 75, 77.