4
Solving Inequalities by
Multiplying or Dividing
Warm Up
Solve each equation.
1.
–5a = 30
3.
2.
4.
Graph each inequality.
5. x ≥ –10
6. x < –3
Holt McDougal Algebra 1
4
Solving Inequalities by
Multiplying or Dividing
Objectives
Solve one-step inequalities by
using multiplication and
division.
Holt McDougal Algebra 1
4
Solving Inequalities by
Multiplying or Dividing
Consider the inequality
41
What if we multiply or divide by a positive
number?
Holt McDougal Algebra 1
4
Solving Inequalities by
Multiplying or Dividing
Example 1: Multiplying or Dividing
by a Positive Number
Solve the inequality and graph the
solutions.
7x > –42
Since x is multiplied
by 7, divide both
sides by 7 to
undo the
multiplication.
–10–8 –6–4 –2 0 2 4 6 8 10
Holt McDougal Algebra 1
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Solving Inequalities by
Multiplying or Dividing
Example 2: Multiplying or Dividing by a
Positive Number
Solve the inequality and graph the
solutions.
Since m is divided
by 3, multiply
both sides by 3
to undo the
division.
m
2 .4 
3
0
2
4
Holt McDougal Algebra 1
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Solving Inequalities by
Multiplying or Dividing
Example 3: Multiplying or Dividing by
a Positive Number
Solve the inequality and graph the
solutions.
Since r is
multiplied by
, multiply both
sides by the
reciprocal of
3
r  12
4
0
2 4
Holt McDougal Algebra 1
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8 10 12 14 16 18 20
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Solving Inequalities by
Multiplying or Dividing
Try it on your Own!!
Solve the inequality and graph the
solutions.
4k > 24
0
2
4
Holt McDougal Algebra 1
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8 10 12 14 16 18 20
4
Solving Inequalities by
Multiplying or Dividing
Consider the inequality
4 2
What if we multiply or divide by a
negative number?
Holt McDougal Algebra 1
4
Solving Inequalities by
Multiplying or Dividing
If you
multiply or
divide by a
negative,
FLIP the
inequality
symbol.
Caution!
Do not change the direction of the
inequality symbol just because you
see a negative sign. For example, you
do not change the symbol when
solving 4x < –24.
Holt McDougal Algebra 1
4
Solving Inequalities by
Multiplying or Dividing
Example 4: Multiplying or Dividing by a
Negative Number
Solve the inequality and graph the
solutions.
–12x > 84
–14 –12 –10 –8 –6 –4 –2
Holt McDougal Algebra 1
Since x is
multiplied by –
12, divide both
sides by –12.
Change > to
<.
0
2
4
6
4
Solving Inequalities by
Multiplying or Dividing
Example 5: Multiplying or Dividing by a
Negative Number
Solve the inequality and graph the
solutions.
x
8 
3
Since x is divided
by –3, multiply
both sides by –
3. Change to
.
10 12 14 16 18 20 22 24 26 28 30
Holt McDougal Algebra 1
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Solving Inequalities by
Multiplying or Dividing
Example 6
A spool of ribbon is 80 inches long.
Hunter needs to cut strips of ribbon
that are 14 inches long. What are the
possible number of strips that riley can
cut? Define a variable, write an
nequality, solve, graph and write a
statement for the solutions.
r=
Holt McDougal Algebra 1
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Solving Inequalities by
Multiplying or Dividing
Assignment
Page 183
#42 - 65
Holt McDougal Algebra 1