Chapter 2.2 and 2.3 Solving Inequalities in One Step.notebook
September 09, 2016
Bellwork:
Add/Subtract:
1)
2)
3)
Homework Questions???
4) Define a variable and write an inequality for the situation. Graph the solutions.
There must be at least 20 club members present to hold a meeting. Sep 4­10:18 AM
Sep 4­10:20 AM
Solve the following equations:
a. x + 5 = 7
Chapter 2.2 and 2.3 Solving Inequalities by Adding or Subtracting and Multiplying or Dividing
Be able to solve one­step inequalities by using addition, subtraction, multiplication and division.
b. y ­ 10 = 5
What steps did you take to solve the equation? Does your answer make sense?
Sep 4­10:20 AM
Sep 8­7:57 AM
We can solve one­step inequalities using the same ideas as solving one step equations. Use inverse operations to "undo" the operation in an inequality.
Problem Solving:
Use addition and subtraction to solve inequalities:
4) Sami has a gift card. She has already used $14 of the total value, which was $30. Write, solve ad graph an inequality to show how much more she can spend.
1) x + 12 < 20
­10
­9
­7
­8
­3
­5 ­4
­6
1
0
­1
­2
2
3
4
5
6
8
7
10
9
2) 0.9 ≥ n ­ 0.3
­5
­2
­3
­4
­1
1
0
2
3
5
4
3) d ­ 5 > ­7
­10
­9
­8
­7
­6
­5 ­4
­3
­2
­1
0
1
Sep 4­10:22 AM
2
3
4
5
6
7
8
9
10
Sep 4­10:26 AM
1
Chapter 2.2 and 2.3 Solving Inequalities in One Step.notebook
September 09, 2016
We are going to transfer the same properties to solve an equation by multiplication and division to inequalities.
Use multiplication/division to solve the following inequalities.
Solve the following equations:
a.
b.
1) What steps did you take to solve the equations? Does your answers make sense? 2)
3)
Sep 8­7:31 AM
Sep 4­10:30 AM
Work with a partner and fill in the appropriate inequality sign:
5
Solve the following inequalities and graph:
8
5(3)
8(3)
5(2)
8(2)
5(1)
8(1)
5(0)
8(0)
5(­1)
8(­1)
5(­2)
8(­2)
5(­3)
8(­3)
5) 6)
What do you notice happens when you multiply by a negative number? What happens when you multiply by 0?
Aug 24­4:30 PM
Aug 24­4:32 PM
Properties of Inequality:
Words
Addition and Subtraction:
You can add or subtract the same number to both sides of an inequality, and the statement will still be true.
Numbers 3 < 8
3 + 2 < 8 + 2
5 < 10
or
3 < 8
3 ­ 2 < 8 ­ 2
1 < 6
Sep 8­7:47 AM
Algebra
a < b
a + c < b + c
or
a < b
a ­ c < b ­ c
Words
Multiplication and Division:
You can multiply or divide both sides of an inequality by the same positive number, and the statement will still be true.
Numbers 3 < 8
3(2) < 8(2)
6 < 16
or 4 < 8
4 ÷ 2 < 8 ÷ 2
2 < 4
Algebra
a < b
a(c) < b(c)
or
a < b
a ÷ c < b ÷ c
Aug 24­4:29 PM
2
Chapter 2.2 and 2.3 Solving Inequalities in One Step.notebook
September 09, 2016
When you multiply or divide both sides by a negative number you have to reverse (flip) the inequality sign.
Properties of Inequality:
Words
Homework:
Numbers Multiplication or Divsion by 3 < 8
negative numbers:
3(­2) > 8(­2)
If you multiply or divide both ­6 > ­16
sides of an inequality by the same negative number, you 4 < 8
must reverse the inequality 4 ÷ ­2 > 8 ÷ ­2
symbol for the statement to be ­2 > ­4
true.
Aug 24­4:31 PM
Algebra
a < b
a(c) > b(c),
or
a < b
a ÷ c > b ÷ c,
Solving One­Step Inequalities
if c is < 0.
Aug 24­4:32 PM
Sep 9­3:35 PM
3