Algebra I
Chapter 2: Inequalities
2.1 – 2.5 Graph, Write, and Solve inequalities
Objectives:
·Graph and write linear inequalities in one variable
· Solve multi-step inequalities.
Warm Up
1) Determine if the number is a solution of the inequality
a) x + 7 < 9
; x=1
b) 4x – 2 > 7 ; x = 2
c)
x + 3 < 6 ; x = 5.
d) 2 x − 3 > −3 ; x = 1.
e) 4 x − 1 ≤ 3 x + 2 ; x = 3.
2) Solve 6x + 8 = 36 + 2x
3) Write the meaning of the inequality symbols in words
<
>
≤
≥
Algebra I
Chapter 2: Inequalities
2.1 – 2.5 Graph, Write, and Solve inequalities
Objectives:
·Graph and write linear inequalities in one variable
· Solve multi-step inequalities.
Graphing Inequalities:
Draw a number line and circle the number in the solution of the inequality. The circle should be
“open” if the inequality has a > or < symbol. The circle should be “closed” if the inequality has
a ≥ or ≤ symbol. A line with an arrow should then be drawn in the appropriate direction
Example 1: Write a verbal phrase to describe the inequality. Then graph the inequality.
Inequality
1) x < 4
2) a > -3
3) z ≤ 0
4) d ≥ -2
5) 3 < x < 5
6) -2 ≤ x ≤ 7
7)
a ≠ 5
Verbal Phrase
Graph
Example 2: Michael can spend at most $3.10 for lunch. He buys a hamburger and a drink for
$2.15. Write an inequality that models how much Michael can spend on dessert and stay within
his spending limit.
Example 3: Solve and graph the inequalities
1)
m–8≥2
2)
5>x–3
3)
m – 3.5 ≤ 2.6
4)
1 3
x+ ≥
2 4
Special Rule with Inequalities: When you multiply or divide by a negative number,
SWITCH THE SIGN!!!!
Why?
Example 4: Solve and graph the inequalities.
1)
3x > 6
2)
16 ≤ 2y
3)
-25 > 5x
4)
a
≥4
3
5)
-x > 9
8)
3x – (2 + 6x) ≤ 28
−2r
≥ −4
7
15 ≤ -5x
7)
9)
-2x – 6 ≥ – 2
10) 10 >
12)
6x – 1 ≤ 3.5x + 4
13) 6(1 – x) < 3x
14)
1.6x ≤ -0.2x + 0.9
15) x + 5 ≥ x + 3
16)
2(x + 3) < 5 + 2x
11)
x < 3x + 8
6)
(! – !!)
!
Example 5: The Daily Mirror charges a fee of $650 plus $80 a week to run an ad. Star charges
$145 per week. For how many weeks will the total cost at the Daily Mirror be less expensive
than the total cost at Star?
You Try: Solve and graph the inequality
1)
c + 7 ≤ -11
2)
3)
6y > 12
4)
18 < 3x
5)
5m ≤ -35
6)
-x < 12
7)
-4x > 24
8)
-16x ≤ -32
9)
x
≥ −6
7
10)
x
≤ −30
−9
11)
2m + 7(m – 1) > 26
12)
-3p + 2 ≤ – 5
13)
-3 > t + 7
2x + 3(x – 2) < – 10
14) 4x ≥ 7x + 6
15)
5t + 1 < -2t – 6
16) 4(y – 1) ≥ 4y + 2
17)
x–2<x+1
Homework: p. 150 # 3 – 60 Multiples of 3