MA112 – 1.6 Solving Linear Inequalities
Today:
1.6: solving linear inequalities
Announcements
 Homework 1.6 due Wed
 quiz next class: solving a compound inequality and sketching it on the real line
Solving simple inequalities.
The rules for solving inequalities are:
(1) You can add or subtract whatever you want to both sides of the equation.
(2) You can multiply both sides of the equation by a positive number.
(3) If you multiply both sides of an equation by a negative number, you must change the direction of the inequality.
Example:
(now add 4 to both sides)
(now subtract 2 from both sides)
(now multiply both sides by 1/2 )
0

10 is true
4

14 is still true
2

12 is still true
1

6 is still true

3
 
18 (multiplying both sides by -3 requires a sign change)
Solving compound inequalities of the form

<

<

Inequalities of this form represent a “conjunctive inequality” where both the left side and the right side must be true.
-4<x<10 means -4<x AND x<10
The rules for solving conjunctive inequalities are:
(1) the same as for simple inequalities, but any operation must be done to every part of the inequality
(2) focus on simplifying the middle part to be ‘x’ or whatever variable you are describing
Intersection and Union of Intervals the intersection of two intervals is where they overlap symbol
 the union of two intervals is their combination symbol
