Transcript Unit 5 Lesson 1: Two

Lesson 3: Two-Step Inequalities
Cornell Notes Header
Topic: Inequalities &
Two-Step Equations
(Unit 7 pg. 3)
Name: _____________________________
Date: _____________________________
Class: _____________________________
How are two-step
inequalities similar to
and different from twostep equations?
Chp. 10 Lesson 5 (6th grade my.hrw.com) –
Two-Step Inequalities
Introduction Problem
 Mr. Smith wants to take his family, a wife and three
children, to the movies. He has at most $62. Seven
dollars will be spent buying the family a snack for the
movie, and the rest will be spent on movie tickets.
What amount can Mr. Smith pay for a movie ticket?
Solving & Graphing Two-Step
Inequalities
1. Solve the two-step inequality just like solving a two- step equation (follow the reverse of
the order of operations).
5t + 7 ≤ 62
-7 -7
5t
55
__ ≤___
5
t
Subtract 7 from both sides.
Divide both sides by 5.
5
≤ 11
2. Graph the solution on a number line. An open (empty) circle signals that the value is
not a solution (use with < & >). A closed (solid) circle signals that the value is a solution
(use with ≥ and ≤).
Graph t ≤ 11. Eleven is a solution to the inequality,
so use a closed circle. Then draw the arrow in the
direction of the numbers that are less than 11.
9
10
11
12
13
14
Problem
 Mr. Smith wants to take his family, a wife and three
children, to the movies. He has at most $62. Seven
dollars will be spent buying the family a snack for the
movie, and the rest will be spent on movie tickets.
What amount can Mr. Smith pay for a movie ticket?
 t ≤ 11 Mr. Smith can pay no more than $11 dollars per
ticket.
 Can Mr. Smith take the family to the movies?
 We cannot determine the answer with the information
given.
Solving and Graphing Two-Step
Inequalities Group Problem

x/
- 6 > 10
+6
+6
x/
> 16
2
2 ∙ x /2
> 16 · 2
x > 32
2
Add 6 to both sides to undo subtracting 6.
Multiply both sides by 2 to undo dividing by 2.
29
 Check:
34/
30
– 6 > 10
17 – 6 > 10
11 > 10
2
31
32
33
34
35
Choose a value larger than 32 to check.
Summary
 Summarize your notes in one to two sentences using
the words two-step inequality and graphing.