UNIT 2 LESSON 4
LINEAR INEQUALITIES
COLLEGE PREP
WARM UP
OBJECTIVES
•Determine whether an ordered pair is a solution to a
linear inequality
•Graph linear inequalities
•Solve problems involving linear inequalities
LINEAR INEQUALITIES
Inequalities:<, ≤, >, ≥
The 𝑥𝑦 region is called a plane.
A line splits the 𝑥𝑦 region into two half planes
A single inequality will look at a combination of the line
and the half plane created by that line.
2𝑥 + 3𝑦 = 6
vs
2𝑥 + 3𝑦 < 6
LINEAR INEQUALITIES
A line is looking for an ordered pair (𝑥, 𝑦) that equals a set
value when substituted into the equation.
ex: 5𝑥 + 2𝑦 = 16 could contain the point (2, 3)
An inequality is looking for an ordered pair that has a
relationship to a set value, but is not necessarily equal to
that value.
LINEAR INEQUALITIES
Find 3 ordered pairs that satisfy the inequality.
A) 3𝑥 + 𝑦 < 7
LINEAR INEQUALITIES
An inequality is the line combined with whichever half
plane is desired.
STEP 1: Graph the line
STEP 2: Determine which half plane is needed and shade
that half plane
NOTE: ≤, ≥ - SOLID LINE
<, > - DASHED LINE
LINEAR INEQUALITIES
Graph.
B) −3𝑥 + 2𝑦 ≤ 3
LINEAR INEQUALITIES
Graph.
C) 4𝑥 + 5𝑦 > 10
LINEAR INEQUALITIES
Graph.
D) 4𝑥 + 3𝑦 < 0
LINEAR INEQUALITIES
Randy knows his lunch intake should not exceed 16 grams
of saturated fat. A cheeseburger contains 6 grams of fat
and a large fry contains 3 grams of fat.
E) Write a linear inequality that describes Randy’s options
for eating.
LINEAR INEQUALITIES
Randy knows his lunch intake should not exceed 16 grams
of saturated fat. A cheeseburger contains 6 grams of fat
and a large fry contains 3 grams of fat.
F) If Randy eats 2 large fries, what is the most number of
cheeseburgers he could eat?
LINEAR INEQUALITIES
Randy knows his lunch intake should not exceed 16 grams
of saturated fat. A cheeseburger contains 6 grams of fat
and a large fry contains 3 grams of fat.
G) Graph Randy’s potential fat intake.
OBJECTIVES
•Determine whether an ordered pair is a solution to a
linear inequality
•Graph linear inequalities
•Solve problems involving linear inequalities
HOMEWORK
In Class Assignment 2.4
Homework 2.4
EDPuzzle 2.4