This document provides instructions for solving linear inequalities in one variable. It explains that to solve an inequality, the same operations can be performed on both sides as with an equation, except that the inequality symbol must be reversed if multiplying or dividing by a negative number. It also describes how to graph the solutions of inequalities on a number line, including whether endpoints are included or excluded. Examples are given of solving and graphing different inequalities on number lines. The homework assignment is to complete problems 1 through 10 on page 97.

1. Solving Linear Inequalities
Pre Calculus Chapter 3, section 1
pp 93 - 98

2. To solve linear inequalities in one variable:
add, subtract, multiply or divide both sides
by the same positive number
multiply or divide both sides by the same
negative number provided you reverse the
inequality symbol

3. Graphing inequalities in one variable on a number line:
Endpoint not included in the solution
Endpoint included in the solution
x≥2
-3 -2 -1 0 1 2 3 4 5 6 7
−2< x ≤ 4
-3 -2 -1 0 1 2 3 4 5 6 7

4. Solve and graph
the solution:
4 x + 7 ≥ 15
4 x + 7 − 7 ≥ 15 − 7
4x ≥ 8
x≥2
1 2 3 4

5. Solve and graph 2+ x 1
the solution: < ( x + 4)
5 3
2+ x 1
15 ⋅ < 15 ⋅ ( x + 4 )
5 3
3( 2 + x ) < 5( x + 4 )
6 + 3 x < 5 x + 20
− 2 x < 14
x > −7
-9 -8 -7 -6 -5 -4 -3

6. Assignment: p 97/1-10 all

7. Assignment: p 97/1-10 all