Download Solving Equations with absolute value and inequalities

Solving Equations with
absolute value and greater
than inequalities
Section 1-7 Algebra II
R. Conyer
EXAMPLE ONE
|X| > 10
If the absolute value equation
contains greater than inequality
then you will set up two
equations.
X > 10 and X < -10 SOLUTION
Step One: Set up the first equation using the original
information. Set up the second equation by changing
the greater than to less than and change positive ten
to negative ten.
EXAMPLE TWO
|X - 4| > 12
Step One:
X – 4 > 12
If the absolute value equation
contains the greater than
inequality then you will set up the
following two equations.
and X – 4 < -12
Step one: Set up the first equation using the original
information. Set up the second equation by changing the
greater than to less than and change positive twelve to
negative twelve.
Step Two: Solve both equations by adding
four to each side of the equations.
X – 4 > 12
+4 +4
0
16
Solution:
X > 16
X – 4 < -12
+4 +4
0
-8
and
X < -8
EXAMPLE THREE
|3X + 7| > 16
Step One:
3X + 7 > 16
and
If the absolute value equation
contains the greater than inequality
then you will set up two equations.
3X + 7 < -16
Step Two: Solve both equations by first subtracting seven
from both sides of the equations.
3X + 7 > 16
-7 -7
0
9
3X > 9
and
3X + 7 < -16
- 7 -7
0
-23
and
3X < -23
Step Three: Solve the equations by dividing by both
sides by three.
3X > 9
3
3
3X < -23
3
3
SOLUTION: X > 3 and
X < -7.67