Algebra 2/Trig
Name: __________________________________
Section 1.7 Notes: Solving Inequalities
p. 54
Objectives: Write, solve, and graph linear inequalities in one variable. Solve and graph compound linear inequalities
in one variable.
INEQUALITY SYMBOLS:
Example 1:
𝟐𝒙 − 𝟓 < 𝒙 + 𝟕
When we solve an inequality in __________ variable, the solution or graph is on a number line. A number line is the
_________________. It includes all ______________________________________.
𝟐𝒙 − 𝟓 < 𝒙 + 𝟕
Open v. Closed
Graph the solution: (Always show ZERO on the number line)
IMPORTANT TO REMEMBER:
When using inequalities, I have to _____________ the inequality when I multiply or divide by a ________________.
Example 2:
𝟔 − 𝟑𝒙 ≤ 𝟔𝒙 + 𝟐𝟓
Graph the solution:
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AND v. OR
COMPOUND INEQUALITIES

Have more than one equation

There are two types of compound inequalities.
o
Disjunction – an __________ statement, either one could be ___________.
o
Conjunction - an __________ statements, BOTH statements must be _________.
Example 3:
𝟐𝐱 < −𝟖 𝐨𝐫 𝐱 ≥ 𝟕
Solve and graph the solution.
Graph the solution:
This is called a ____________________________________________________________.
Example 4:
𝒙 > −𝟐 𝒂𝒏𝒅 𝒙 < 𝟓
CONJUNCTION
You can write the solution as _______________________________________________.
A disjunction cannot be written this way, it must include _______________________.
Example 5:
−𝟕 ≤ 𝟐𝒙 − 𝟓 ≤ 𝟗
You can do this in two parts or simultaneously.
In two parts:
−7 ≤ 2𝑥 − 5
Simultaneously:
2𝑥 − 5 ≤ 9
−7 ≤ 2𝑥 − 5 ≤ 9
Graph:
______________________________________________________________________________________________
1.7 HW: Pages 58 & 59 - Problems 12 – 72 (3rds) and 73 - 75
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