Multistep Equations and Inequalities

1
Chapter 11

• Multi-step Equations and Inequalities

2
Just to Get You Thinking

• Can you think of any activities that require
  following a certain order to get a desired
  outcome?

3
11-1 Solving Two Step Equations

• Follow the order of operations in reverse order
• Undo subtraction and addition first
• Undo multiplication and division second

4
Solving Using Division

• 6n 4 28
• -3p 8 19

5
Solving Using Multiplication

• 8 j/4 17
• u/6 12 3

6
More Practice

• 9c 3 39
• -4m 6 -34

7
More Practice

• 6 y/5 21
• x/7 11 9

8
Consumer Math Application

• A new one-year membership at Gold Gym costs 630.
  A registration fee of 150 is paid up front, and
  the rest is paid monthly. How much do new
  members pay each month?
• 12m 150 630

9
Problem Solving

• Two years of local Internet service costs 685,
  including the installation fee of 85. What is
  the monthly fee?

10
Think and Discuss

• Explain how you decide which inverse operation to
  do first in a two-step equation.

11
11-2 Solving Multi-step Equations

• Do you remember how to combine like terms?
• 2a 6 5a 3 b

12
Solving With Like Terms

• Clean up the problem first by combining like
  terms
• 7n 1 2n 14
• 12 7b 10b 18

13
Solving Equations with Fractions

• Undo the fraction first by multiplying both sides
  by the denominator
• 4x 8 12
• 9

14
Solving Equations with Fractions

• 3y 6 3
• 7
• 3w .5 1
• 2

15
Problem Solving

• Marcella has twice as many movies as Jenn owns.
  Adding 6 to the number of movies Marcella owns
  and then dividing by 7 gives the number that
  Brandon owns. If Brandon owns 30 movies, how
  many does Jenn own?

16
Make a Plan

• List the important information
• Write your own equation
• Solve

17
Think and Discuss

• List the steps required to solve n 5n 3 27
• Describe how to solve 2x 7 4
• 3

18
11-3 Solving Equations with Variables on Both
Sides

• Group the terms with variables on one side of the
  equal side and simplify
• 6m 4m 12

19
Grouping Terms with Variables

• -7x 198 5x
• 60 4y 8y

20
Solving Equations with Variables on Both Sides

• 5n 3n 26
• 19 7n -2n 37

21
More Practice

• 5/9x 4/9x 9
• 2/5x 1/5x - 12

22
More Practice

• -5b 72 -2b
• 49 3m 4m 14

23
Think and Discuss

• Explain how you would solve
• 1/2 x 7 2/3x -2

24
11-4 Inequalities
25
Writing Inequalities

• There are at least 25 students in the auditorium.
• No more than 150 people can occupy the room.
• There are at least 15 people in the waiting room.

26
Graphing Simple Inequalities

• Solution set all the solutions for an
  inequality
• Open dot is not a solution, used for lt and gt
• Closed dot is a solution, used for and

27
Graphing

• X gt -2
• Y -1
• N lt 3
• A -4

28
Compound Inequalities

• S 0 or S lt -3
• 1 lt P 5

29
Practice

• M -2 or M gt 1
• -3 lt B 0

30
Think and Discuss

• Compare the graphs for the inequalities y gt 2 and
  y 2