Lesson 9.8 Solving Two-Step Inequalities

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Warm Up Solve each equation.
1. 2x 5 17 2.
6
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Solve each inequality and graph the solutions.
t gt 4
3. 5 lt t 9
4.
a 8
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Lesson 3.4 Solving Two-Step and multi-step
Inequalities
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Objectives

• Solve inequalities that contain more than one
  operation

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Inequalities that contain more than one operation
require more than one step to solve. Use inverse
operations to undo the operations in the
inequality one at a time.
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Steps to solve a Two-step inequality
Step 1 Undo addition or subtraction
Step 2 Undo multiplication and division
Is your variable isolated?
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Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
45 2b gt 61
1. Add/ Subtract
2. Multiply/Divide
2b gt 16
The solution set is bb gt 8.
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Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
1. Add/Subtract
8 3y 29
2. Multiply/Divide
3y 21
The solution set is yy ? 7.
y 7
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The Box Method

• Lets try to solve backwards 6x 11 lt 13

X lt 4
6
- 11
x
?
13
11
6
13
24
4
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You try

• Solve and Graph the inequality

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To solve more complicated inequalities, you may
first need to simplify the expressions on one or
both sides.
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Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
2 (10) gt 4t
1. Combine like terms.
12 gt 4t
2. Multiply/Divide
3 lt t
(or t gt 3)
The solution set is tt gt 3.
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Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
4(2 x) 8
1. Distributive Property
-4(2 x) 8
-4(2) - 4(-x) 8
2. Add/Subtract
3. Multiply/Divide
4x 16
x 4
The solution set is xx 4.

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Word Problem
The average of Jims two test scores must be at
least 90 to make an A in the class. Jim got a 95
on his first test. What grades can Jim get on his
second test to make an A in the class?
Let x represent the test score needed. The
average score is the sum of each score divided by
2.
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Word Problem Continued
Since 95 x is divided by 2, multiply both sides
by 2 to undo the division.
95 x 180
Since 95 is added to x, subtract 95 from both
sides to undo the addition.
x 85
The score on the second test must be 85 or
higher.
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Now you try
1. 3x 7 gt 2 4. x 4 lt 3 5 2. 4x
1 ? -3
5. 15 x 6 3 3. 2x 7 -3
x gt 3
x lt 35
x -1
x -27
x 2
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Lesson Quiz Part I
Solve each inequality and graph the solutions.
1. 13 2x 21
x 4
2. 11 2 lt 3p
p gt 3
t gt 7
3. 23 lt 2(3 t)
4.
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Lesson Quiz Part II
5. A video store has two movie rental plans. Plan
A includes a 25 membership fee plus 1.25 for
each movie rental. Plan B costs 40 for unlimited
movie rentals. For what number of movie rentals
is plan B less than plan A?
more than 12 movies