Chapter 2.4(a) Linear Inequalities and Problem Solving.notebook
September 15, 2016
Bellwork:
Multiply/Divide
1)
2)
3)
Chapter 2.4 Linear Inequalities and Problem Solving
Be able to write and graph inequalities using interval notation. Solve:
4) Aug 22­12:18 PM
Linear Inequality in One Variable:
A linear inequality in one variable is an inequality that can be written in the form:
ax + b < c
where a, b, and c are real numbers and a ≠ 0.
Solution to an Inequality: is any value of the variable that makes the inequality true.
Solution Set: set of all solutions of the inequality
Aug 22­12:19 PM
Inequalities like x < 3 and y ≥ ­4 have too many solutions to list, instead we use a number line to graph all the solutions.
How would we graph the solutions for {x x < 3}?
Aug 22­12:19 PM
Symbol
<
>
≤
≥
≠
Meaning
A < B = A is less than B.
A > B = A is greater than B.
A ≤ B = A is less than or equal to B.
A ≥ B = a is greater than or equal to B.
A ≠ B = A is not equal to B.
Aug 22­12:19 PM
We have been using set notation to write the solutions to equations. We are going to shift from set notation to interval notation.
When using interval notation we switch form using open and closed circles to () and [] to show if an inequality is open of closed.
Graph {x x < 3} using interval notation symbols?
How would we graph the solutions for {y y ≥ ­4}?
Graph {y y ≥ ­4} using interval notation symbols?
Aug 22­12:21 PM
Aug 22­12:23 PM
1
Chapter 2.4(a) Linear Inequalities and Problem Solving.notebook
September 15, 2016
Write the set and interval notation for the following number lines:
Hint: Read the line left to right and fill in what you see. Arrow = ∞.
]
1)
­5
2)
­4
a. {x x ≤ 0}
(
­3
­2
­1
1
0
2
3
Graph each set on a number line and then write in interval notation.
4
5
c. {x ­0.5 ≤ x < 2}
(
­5
­4
­3
­2
­1
0
1
2
­5
­4
­3
­2
­1
0
1
2
3)
3
4
5
4
5
]
3
Aug 22­12:30 PM
Aug 22­12:33 PM
Examples from book (page 77): Set Notation
Graph
Interval Notation
{x x < a}
(
{x x > a}
(
(a, ∞)
{x x ≤ a}
[
(­∞, a]
(­∞, a)
a
a
a
{x x ≥ a}
(
{x a < x < b}
(
a
b
{x a ≤ x ≤ b}
[
[
a
b
(
[
a
1) 3/4 < a
[a, ∞)
[
a
{x a < x ≤ b}
What do you do if the variable is on the right side instead of the left? Graph and write the following inequalities in interval notation.
2) 5(­1 + 3) ≥ m
(a, b)
[a, b]
(a, b]
b
Aug 22­12:31 PM
Aug 22­12:28 PM
Homework:
Writing in Interval Notation
Aug 22­12:36 PM
Sep 15­9:52 AM
2