Transcript Holt McDougal Algebra 1

Solving
Two-Step
Solving
Two-Step
and and
4.1/5.1
Multi-Step
Inequalities
Multi-Step
Inequalities
Warm Up
Lesson Presentation
Lesson Quiz
Holt
1 Algebra 1
HoltAlgebra
McDougal
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Warm Up
Graph each inequality.
1. x ≥ –10
Holt McDougal Algebra 1
2. x < –3
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 1
Solve the inequality and graph the solutions.
45 + 2b > 61
45 + 2b > 61
–45
–45
Since 45 is added to 2b,
subtract 45 from both sides
to undo the addition.
2b > 16
b>8
0
2
4
6
Since b is multiplied by 2, divide
both sides by 2 to undo the
multiplication.
8 10 12 14 16 18 20
Holt McDougal Algebra 1
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 2
Solve the inequality and graph the solutions.
8 – 3y ≥ 29
8 – 3y ≥ 29
–8
–8
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
–7
–10 –8 –6 –4 –2
Holt McDougal Algebra 1
0
2
4
6
8 10
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 3
Solve the inequality and graph the solutions.
–12 ≥ 3x + 6
–12 ≥ 3x + 6
–6
–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
–10 –8 –6 –4 –2
Holt McDougal Algebra 1
0
2
4
6
8 10
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 4
Solve the inequality and graph the solutions.
Since x is divided by –2, multiply
both sides by –2 to undo the
division. Change > to <.
x + 5 < –6
–5 –5
Since 5 is added to x, subtract 5
from both sides to undo the
addition.
x < –11
–11
–20
–16
–12
Holt McDougal Algebra 1
–8
–4
0
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
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.
Holt McDougal Algebra 1
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 5
Solve the inequality and graph the solutions.
3 + 2(x + 4) > 3
Distribute 2 on the left side.
3 + 2(x + 4) > 3
3 + 2x + 8 > 3
Combine like terms.
Since 11 is added to 2x, subtract
11 from both sides to undo the
addition.
2x + 11 > 3
– 11 – 11
2x
> –8
Since x is multiplied by 2, divide
both sides by 2 to undo the
multiplication.
x > –4
–10 –8 –6 –4 –2
Holt McDougal Algebra 1
0
2
4
6
8 10
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 6
Solve the inequality and graph the solutions.
Multiply both sides by 8, the LCD
of the fractions.
Distribute 8 on the right side.
5 < 3x – 2
+2
+2
7 < 3x
Holt McDougal Algebra 1
Since 2 is subtracted from 3x,
add 2 to both sides to undo
the subtraction.
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 7
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 is 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.
Cost at
Rent-ARide
must be
less
than
55
<
Holt McDougal Algebra 1
daily
cost at
We Got
Wheels
38
plus
+
$0.20
per mile
0.20
times
# of
miles.

m
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 7 Continued
55 < 38 + 0.20m
Since 38 is added to 0.20m, subtract
55 < 38 + 0.20m
38 from both sides to undo the
addition.
–38 –38
17 < 0.20m
Since m is multiplied by 0.20, divide
both sides by 0.20 to undo the
multiplication.
85 < m
Rent-A-Ride costs less when the number of miles is
more than 85.
Holt McDougal Algebra 1
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 7 Continued
Check
Check the endpoint, 85.
Check a number greater
than 85.
55 = 38 + 0.20m
55 < 38 + 0.20m
55
38 + 0.20(85)
55 < 38 + 0.20(90)
55
55
38 + 17
55 
55 < 38 + 18
55 < 56 
Holt McDougal Algebra 1
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 8
The average of Jim’s 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.
First
test
score
(95
plus
second
test
score
+
Holt McDougal Algebra 1
x)
divided
by

number
of scores
2
is greater
than or
equal to
≥
total
score
90
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 8 Continued
Since 95 + x is divided by 2, multiply
both sides by 2 to undo the division.
95 + x ≥ 180
–95
–95
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.
Holt McDougal Algebra 1
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Example 8 Continued
Check
Check the end point,
85.
Check a number greater
than 85.
90
90
90
90

Holt McDougal Algebra 1
90.5 ≥ 90 
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
Lesson Quiz: Part I
Solve each inequality and graph the solutions.
1. 13 – 2x ≥ 21 x ≤ –4
2. –11 + 2 < 3p
p > –3
3. 23 < –2(3 – t)
t>7
4.
Holt McDougal Algebra 1
Solving Two-Step and
4.1/5.1
Multi-Step Inequalities
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
Holt McDougal Algebra 1