Download Lesson 2

Solving Two-Step and
2-4 Multi-Step Inequalities
Warm Up 10/27
Solve each equation.
1. 2x – 5 = –17 –6
2.
Holt McDougal Algebra 1
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Solving Two-Step and
2-4 Multi-Step Inequalities
Take out what you have so far from
yesterday’s Problem Solving Worksheet.
Get as far as you can in the next 10
minutes
If you finish, raise your hand and I will
tell you what to do next!!
Holt McDougal Algebra 1
Solving Two-Step and
2-4 Multi-Step Inequalities
Objective
Solve inequalities that contain more than one
operation.
Holt McDougal Algebra 1
Solving Two-Step and
2-4 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 McDougal Algebra 1
Solving Two-Step and
2-4 Multi-Step Inequalities
What you need…….TURN IN PRACTICE B from
Section 2-3
PHONES AWAY
Warm-Up Sheet and Work from Problem Solving
yesterday!
Pencil/Pen
Notes
Holt McDougal Algebra 1
Solving Two-Step and
2-4 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
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
2-4 Multi-Step Inequalities
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 > 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
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–4
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Solving Two-Step and
2-4 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
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Solving Two-Step and
2-4 Multi-Step Inequalities
Check It Out! Example 1c
Solve the inequality and graph the solutions.
1 – 2n ≥ 21
–1
–1
–2n ≥ 20
Since 1 – 2n is divided by 3,
multiply both sides by 3 to
undo the division.
Since 1 is added to –2n, subtract
1 from both sides to undo the
addition.
Since n is multiplied by –2, divide
both sides by –2 to undo the
multiplication. Change ≥ to ≤.
n ≤ –10
–10
–20
Holt McDougal Algebra 1
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–12
–8
–4
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Solving Two-Step and
2-4 Multi-Step Inequalities
What you need…….MAKE SURE YOU HAVE
TURNED IN:
1) Practice 2-3 Worksheet
2) TURN IN Warm-Up sheet from this week
PHONES AWAY
Pencil/Pen
Notecard for Quiz!
Holt McDougal Algebra 1
Solving Two-Step and
2-4 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 McDougal Algebra 1
Solving Two-Step and
2-4 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
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Solving Two-Step and
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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
–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
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Solving Two-Step and
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Check It Out! Example 2a
Solve the inequality and graph the solutions.
2m + 5 > 52
2m + 5 > 25
–5>–5
2m
> 20
m > 10
0
2
4
6
Simplify 52.
Since 5 is added to 2m, subtract 5
from both sides to undo the
addition.
Since m is multiplied by 2, divide
both sides by 2 to undo the
multiplication.
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Holt McDougal Algebra 1
Solving Two-Step and
2-4 Multi-Step Inequalities
Check It Out! Example 2b
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
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Solving Two-Step and
2-4 Multi-Step Inequalities
Exit Ticket:
1) What is one thing you want me to
know about you that I don’t already
know?
Holt McDougal Algebra 1