Solving
Two-Step
Solving
Two-Step
and and
3-4 Multi-Step Inequalities
3-4
Multi-Step Inequalities
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Holt
Algebra
Algebra
1 1
Solving Two-Step and
3-4 Multi-Step Inequalities
Warmup
Solve each inequality and graph the solutions.
1. 8x < –24 x < –3
2. –5x ≥ 30
x ≤ –6
3.
4.
x≥6
x > 20
5. A soccer coach plans to order more shirts for
her team. Each shirt costs $9.85. She has $77
left in her uniform budget. What are the
possible number of shirts she can buy?
0, 1, 2, 3, 4, 5, 6, or 7 shirts
Holt Algebra 1
Solving Two-Step and
3-4 Multi-Step Inequalities
Warmup
• Quiz – Start NOW
Holt Algebra 1
Solving Two-Step and
3-4 Multi-Step Inequalities
Warm Up
Solve each equation.
1. 2x – 5 = –17 –6
2.
14
Solve each inequality and graph the
solutions.
3. 5 < t + 9 t > –4
4.
Holt Algebra 1
a ≤ –8
Solving Two-Step and
3-4 Multi-Step Inequalities
Objective
Solve inequalities that contain more than one
operation.
Holt Algebra 1
Solving Two-Step and
3-4 Multi-Step Inequalities
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.
Holt Algebra 1
Solving Two-Step and
3-4 Multi-Step Inequalities
Example 1A: Solving Multi-Step Inequalities
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
Holt Algebra 1
6
Since b is multiplied by 2, divide
both sides by 2 to undo the
multiplication.
8 10 12 14 16 18 20
Solving Two-Step and
3-4 Multi-Step Inequalities
Example 1B: Solving Multi-Step Inequalities
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 Algebra 1
0
2
4
6
8 10
Solving Two-Step and
3-4 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 Algebra 1
Solving Two-Step and
3-4 Multi-Step Inequalities
Example 2A: Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
2 – (–10) > –4t
12 > –4t
Combine like terms.
Since t is multiplied by –4, divide
both sides by –4 to undo the
multiplication. Change > to <.
–3 < t (or t > –3)
–3
–10 –8 –6 –4 –2
Holt Algebra 1
0
2
4
6
8 10
Solving Two-Step and
3-4 Multi-Step Inequalities
Example 2B: Simplifying Before Solving Inequalities
Solve the inequality and graph the solutions.
–4(2 – x) ≤ 8
−4(2 – x) ≤ 8
−4(2) − 4(−x) ≤
8
–8 + 4x ≤ 8
+8
+8
4x ≤ 16
Distribute –4 on the left side.
Since –8 is added to 4x, add 8 to
both sides.
Since x is multiplied by 4, divide
both sides by 4 to undo the
multiplication.
x≤4
–10 –8 –6 –4 –2
Holt Algebra 1
0
2
4
6
8 10
Solving Two-Step and
3-4 Multi-Step Inequalities
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 > 2
–3 –3
4f
Holt Algebra 1
> –1
Since 3 is added to 4f, subtract 3
from both sides to undo the
addition.
Solving Two-Step and
3-4 Multi-Step Inequalities
Example 2C Continued
4f > –1
Since f is multiplied by 4, divide both
sides by 4 to undo the
multiplication.
0
Holt Algebra 1
Solving Two-Step and
3-4 Multi-Step Inequalities
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.
Cost at
Rent-ARide
must be
less
than
55
<
Holt Algebra 1
daily
cost at
We Got
Wheels
38
plus
+
$0.20
per mile
0.20
times
# of
miles.

m
Solving Two-Step and
3-4 Multi-Step Inequalities
Example 3 Continued
55 < 38 + 0.20m
Since 38 is added to 0.20m, subtract 8
55 < 38 + 0.20m
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 Algebra 1
Solving Two-Step and
3-4 Multi-Step Inequalities
Example 3 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 Algebra 1
Solving Two-Step and
3-4 Multi-Step Inequalities
Assignment:
• L3-4 pg 191 #18-72x3, add #37, 83
Holt Algebra 1
Solving Two-Step and
3-4 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 Algebra 1
Solving Two-Step and
3-4 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 Algebra 1