1.7 Absolute Value Equations and Inequalities
General Form:
ax + b > c
The solution set for this general form is the union of two sets, namely,
ax + b > c
or
ax + b < !c
When you solve inequalities of this form, rewrite the original inequality as the union of
two separate inequalities. Solve and graph the union of the solution sets. Write the
solution set using set notation.
Example:
"3x + 4 # 5
!
General Form:
ax + b < c
The solution set for this general form is the intersection of two sets, namely,
! c < ax + b
and
ax + b < c
which can be written more simply as
! c < ax + b < c
When you solve inequalities of this form, rewrite the original inequality as the union of
two separate inequalities. Solve and graph the intersection of the solution sets. Write the
solution set using set notation.
Example:
4x + 3 " 7
!
Practice Problems:
1.)
1
x!3 = 2
`2
2.) 2 x + 7 < 11
3.) "3x + 10 > 7
!
4.) "x + 5 # 6
!
5.)
2x " 1 " 4 ! 2
6.) 4 2 y ! 7 + 5 < 9
Try solving the below two problems using the methods above and also by guessing
and checking numbers. What are the solution sets for each? Why?
a. 3 x ! 5 < !1
b. 3 x ! 5 > !1
c. 2 x " 1 ! 0
d. x ! 3 > 0
Homework: p.53-54 #33-39 odd, 47-58 All