Transcript Unit 5 Lesson 1: Two

Lesson 2: One-Step Inequalities
Cornell Notes Header
Topic: Inequalities &
Two-Step Equations
(Unit 7 pg. 2)
Name: _____________________________
Date: _____________________________
Class: _____________________________
E.Q.: How are one-step
equations similar and
different than one-step
inequalities?
Chp. 10 Lesson 4 (6th Grade my.hrw.com) –
One-Step Inequalities
Vocabulary
 inequality – A statement that two quantities are not equal.
The quantities are compared using >, <, ≤, ≥, & ≠.
 solution of an inequality – Any value of the variable that
makes the statement true. Inequalities can have more than
one solution.
x
x>5
Solution
0
0>5
No
5
5>5
No
7.5
7.5 > 5
Yes
14
14 > 5
Yes
Group Word Problem
 Melissa made $35 dollars babysitting two children for
seven hours. She needs at least $199 for a new IPOD.
At a minimum, how much more money does Melissa
need to buy the IPOD? Write and solve a one-step
inequality.
 n + 35 ≥ 199
where n = money still needed
Solving & Graphing One-Step
Inequalities
1. Solve the inequality just like solving a one- step equation.
(Use the inverse operation to undo the current operation.)
n + 35 ≥ 199
Subtract 35 from both sides.
- 35 - 35
n ≥ 164
2. Graph the solution on a number line. An open (empty) circle signals that the value is
not a solution (use with < & >). An closed (solid) circle signals that the value is a solution
(use with ≥ and ≤).
Graph n ≥ 164. 164 is a solution to the inequality,
so use a closed circle. Then draw the arrow in the
direction of the numbers that are larger than 164.
162
163
164 165 166
Solving and Graphing One-Step
Inequalities Example

w ≤ 4
1
2
3
4
5
6
7
Solving and Graphing One-Step
Inequalities Example

4 ≤ n–3
+3 +3
7 ≤ n which is n ≥ 7
4
5
Undo the subtraction with addition.
6
7
8
9
10
Solving and Graphing One-Step
Inequalities Example

x/
6
6
> 2
· x/6 > 2 · 6
x > 12
Undo the division with multiplication.
9
10
11
12
13
14
15
Solving and Graphing One-Step
Inequalities Example

5p ≤ 45
5p ≤ 45
5
5
p ≤ 9
Undo the multiplication with division.
6
7
8
9
10
11
12
Inequality Key Words For Solving
Word Problems
Words
Symbol
Example
less than
<
x is less than 8
x<8
greater than
>
x is greater than 12
x > 12
less than or equal to
≤
x is less than or equal to 2
x≤2
greater than or equal to
≥
x is greater than or equal to 7
x≥7
at most
≤
I need at most $15 for drinks at Sea World.
x ≤ 15
at least
≥
I need at least $10 for the movie.
no less than
≥
I need no less than $10 a week for lunch.
x ≥ 10
no more than
≤
I need no more than $10 to get lunch at
McDonalds.
x ≤ 10
between
<x<
I need between $10 and $20 for the movie.
10 < x < 20
x ≥ 10
Summary
 Summarize your notes in one to two sentences using
the words one-step inequality, open circle, closed
circle, and graphing.