Download Linear Inequalities in One Variable

Activating Prior Knowledge
Plot the following numbers on the number line and
label.
−𝟕
𝟏𝟐
𝟓
-7
1.2
𝟑
𝟐
𝟒
Solving Linear Inequalities
in One Variable
AA1CC
Solutions
The solution to an inequality is
the set of all numbers that make
the statement true.
Big Ideas (Graphing)
Graphing Practice
a. Graph −𝟐 < 𝒙
b.What inequality is the graph representing?
A few more: Write the Inequality the graph
is representing
C.
D.
E.
F.
Big Ideas (Solving)
 Use same steps as if you were
solving an equation.
 While solving your inequality, if you
multiply or divide both sides of the
inequality by a negative numberreverse (flip) your inequality sign.
#1.Easier (Worked Out) Examples
#2. More Difficult (Worked Out) Example
a.
b.
Ex.1 Solve the Inequality and Graph.
𝟓 < 𝟑𝐱 − 𝟐𝟖
Ex.2 Solve the Inequality and Graph.
−𝟒
𝐫 ≥ −𝟑
𝟕
Ex.3 Solve the Inequality and Graph.
𝟐𝒙 − 𝟔 ≥ 𝟑𝒙 − 𝟐
Ex.4 Solve the Inequality and Graph.
𝟑𝒙 − (𝟐 + 𝟔𝒙) ≤ 𝟐𝟖
Practice #1 Solve and Graph.
Put them on the same graph in different colors.
a. 𝟒𝒎 + 𝟏 < 𝟓𝒎 − 𝟕 b. 𝟑𝒙 − 𝟐 𝒙 + 𝟒 ≤ 𝟑𝒙 − 𝟖
Homework
Red Workbook
p.90 #1-10 all
Is there always one solution?
No 
1. If an ineqality is equivalent to an inequality that is
false (Ex. 5>10), then the inequality has no solution.
2. If an inequality is equivalent to an inequality that is
true (Ex. -3<0), then the solutions to the inequality are
all real numbers.
Ex. 5 Solve the inequality.
a. 14x + 5 < 7(2x-3)
b. 12x-1 > 6(2x-1)
Compound Inequalities
A compound inequality consists
of two separate inequalities
joined by and or or.
Compound Inequalities Graph Examples
Worked Out Example: Translating from
Words to Inequalities
Ex.1 Translate and Graph
1.
All real numbers that are less than -1 or greater
than or equal to 4.
2. All real numbers that are greater than or equal to -3
and less than 5
Ex.2 Solve and Graph a Compound Inequality
with and
2<x+5<9
You Try!
a. 10 ≤ 2𝑦 + 4 < 24
b. −7 < −𝑧 − 1 < 3
Ex.3 Solve and Graph a Compound Inequality
with or
2𝑥 + 3 < 9
or
3𝑥 − 6 > 12
You Try!
3ℎ + 1 < −5
𝒐𝒓
2ℎ − 5 > 7
Homework
Red Workbook
p.90 #11-23 odd;
p.93-94 #4-11 all