Warm Up

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Warm Up
Lesson Presentation
Lesson Quiz
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Warm Up Solve each equation.
1. 2x 5 17 2.
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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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Objective
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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Example 1A Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
45 2b gt 61
Since 45 is added to 2b, subtract 45 from both
sides to undo the addition.
2b gt 16
Since b is multiplied by 2, divide both sides by
2 to undo the multiplication.
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Solving a multistep inequality uses the same
inverse operations as solving a multistep
equation. Multiplying or dividing the inequality
by a negative number reverses the inequality
symbol.
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Example 1B Solving Multi-Step Inequalities
Solve the inequality and graph the solutions.
8 3y 29
Since 8 is added to 3y, subtract 8 from both
sides to undo the addition.
3y 21
Since y is multiplied by 3, divide both sides by
3 to undo the multiplication. Change to .
y 7
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Check It Out! Example 1a
Solve the inequality and graph the solutions.
12 3x 6
Since 6 is added to 3x, subtract 6 from both
sides to undo the addition.
18 3x
Since x is multiplied by 3, divide both sides by
3 to undo the multiplication.
6 x
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Check It Out! Example 1b
Solve the inequality and graph the solutions.
Since x is divided by 2, multiply both sides by
2 to undo the division. Change gt to lt.
Since 5 is added to x, subtract 5 from both sides
to undo the addition.
x lt 11
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Check It Out! Example 1c
Solve the inequality and graph the solutions.
Since 1 2n is divided by 3, multiply both sides
by 3 to undo the division.
1 2n 21
Since 1 is added to -2n, subtract 1 from both
sides to undo the addition.
2n 20
Since n is multiplied by -2, divide both sides by
-2 to undo the multiplication. Change to .
n 10
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To solve more complicated inequalities, you may
first need to simplify the expressions on one or
both sides by using the order of operations,
combining like terms, or using the Distributive
Property.
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Example 2A Simplifying Before Solving
Inequalities
Solve the inequality and graph the solutions.
2 (10) gt 4t
12 gt 4t
Combine like terms.
Since t is multiplied by 4, divide both sides by
4 to undo the multiplication. Change gt to lt.
3 lt t
(or t gt 3)
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Example 2B Simplifying Before Solving
Inequalities
Solve the inequality and graph the solutions.
4(2 x) 8
-4(2 x) 8
Distribute 4 on the left side.
-4(2) - 4(-x) 8
Since 8 is added to 4x, add 8 to both sides.
4x 16
Since x is multiplied by 4, divide both sides by
4 to undo the multiplication.
x 4
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Example 2C Simplifying Before Solving
Inequalities
Solve the inequality and graph the solutions.
Multiply both sides by 6, the LCD of the
fractions.
Distribute 6 on the left side.
4f 3 gt 2
Since 3 is added to 4f, subtract 3 from both
sides to undo the addition.
4f gt 1
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Example 2C Continued
4f gt 1
Since f is multiplied by 4, divide both sides by
4 to undo the multiplication.
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Check It Out! Example 2a
Solve the inequality and graph the solutions.
2m 5 gt 52
Simplify 52.
2m 5 gt 25
Since 5 is added to 2m, subtract 5 from both
sides to undo the addition.
2m gt 20
Since m is multiplied by 2, divide both sides by
2 to undo the multiplication.
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Check It Out! Example 2b
Solve the inequality and graph the solutions.
3 2(x 4) gt 3
Distribute 2 on the left side.
3 2(x 4) gt 3
3 2x 8 gt 3
Combine like terms.
2x 11 gt 3
Since 11 is added to 2x, subtract 11 from both
sides to undo the addition.
2x gt 8
Since x is multiplied by 2, divide both sides by
2 to undo the multiplication.
x gt 4
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Check It Out! Example 2c
Solve the inequality and graph the solutions.
Multiply both sides by 8, the LCD of the
fractions.
Distribute 8 on the right side.
5 lt 3x 2
Since 2 is subtracted from 3x, add 2 to both
sides to undo the subtraction.
2 2
7 lt 3x
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Check It Out! Example 2c Continued
Solve the inequality and graph the solutions.
7 lt 3x
Since x is multiplied by 3, divide both sides by
3 to undo the multiplication.
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Example 3 Application
To rent a certain vehicle, Rent-A-Ride charges
55.00 per day with unlimited miles. The cost of
renting a similar vehicle at We Got Wheels is
38.00 per day plus 0.20 per mile. For what
number of miles in the cost at Rent-A-Ride less
than the cost at We Got Wheels?
Let m represent the number of miles. The cost for
Rent-A-Ride should be less than that of We Got
Wheels.
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Example 3 Continued
55 lt 38 0.20m
Since 38 is added to 0.20m, subtract 8 from both
sides to undo the addition.
17 lt 0.20m
Since m is multiplied by 0.20, divide both sides
by 0.20 to undo the multiplication.
85 lt m
Rent-A-Ride costs less when the number of miles
is more than 85.
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Example 3 Continued
Check
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Check It Out! Example 3
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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Check It Out! Example 3 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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Check It Out! Example 3 Continued
Check
Check a number greater than 85.
Check the end point, 85.
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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