3. Introduction
Inequalities are similar to equations in that they are
mathematical sentences. They are different in that they are
not equal all the time. An inequality has infinite solutions,
instead of only having one solution like a linear equation.
Setting up the inequalities will follow the same process as
setting up the equations did. Solving them will be similar, with
two exceptions, which will be described later.
The prefix in- in the word inequality means “not.” Remember
that the symbols >, <, ≥, ≤, and ≠ are used with inequalities.
1.2.2: Creating Linear Inequalities in One Variable
3
4. Key Concepts, continued
1.2.2: Creating Linear Inequalities in One Variable
Symbol Description Example Solution
>
greater than,
more than
x > 3
all numbers greater than 3;
doesn’t include 3
≥
greater than or
equal to, at least
x ≥ 3
all numbers greater than or
equal to 3; includes 3
< less than x < 3
all numbers less than 3;
does not include 3
≤
less than or
equal to, no
more than
x ≤ 3
all numbers less than or
equal to 3; includes 3
≠ not equal to x ≠ 3 includes all numbers except 3
4
5. Vocabulary
< >
Less than Greater than At most At least
Fewer than More than No more
than
No less
than
Under Over Maximum Minimum
Below Above
6. Key Concepts, continued
• Solving a linear inequality is similar to solving a linear
equation.
• The processes used to solve inequalities are the
same processes that are used to solve equations.
• Multiplying or dividing both sides of an inequality
by a negative number requires reversing the
inequality symbol.
1.2.2: Creating Linear Inequalities in One Variable
6
7. Examples:
Create an expression to represent each of the following:
A number and 20 can be no more than 41
Four times some number is at most 16
The minimum value of a number is 84
45 is more than a number
7
8. Key Concepts, continued
8
Creating Inequalities from Context
1. Read the problem statement first.
2. Reread the scenario and make a list or a table of
the known quantities.
3. Read the statement again, identifying the unknown
quantity or variable.
4. Create expressions and inequalities from the
known quantities and variable(s).
5. Solve the problem.
6. Interpret the solution of the inequality in terms of
the context of the problem.
9. Guided Practice
Example 1
Juan has no more than $50 to spend at the mall. He
wants to buy a pair of jeans and some juice. If the sales
tax on the jeans is 4% and the juice with tax costs $2,
what is the maximum price of jeans Juan can afford?
1.2.2: Creating Linear Inequalities in One Variable
9
10. Guided Practice: Example 1, continued
1. Read the problem statement first.
2. Reread the scenario and identify the known
quantities.
• Juan has no more than $50.
• Sales tax is 4%.
• Juice costs $2.
3. Read the statement again, identify the unknown
quantity.
cost of the jeans
1.2.2: Creating Linear Inequalities in One Variable
Juan has no more than $50 to spend at the mall. He
wants to buy a pair of jeans and some juice. If the sales
tax on the jeans is 4% and the juice with tax costs $2,
what is the maximum price of jeans Juan can afford?
10
11. 1.2.2: Creating Linear Inequalities in One Variable
Guided Practice: Example 1, continued
4. Create expressions and inequalities from the
known quantities and variable(s).
x + 0.04x + 2 ≤ 50
11
Known Unknown
4% sales tax
Cost of jeansJuice costs $2
No more than $50
12. 1.2.2: Creating Linear Inequalities in One Variable
Guided Practice: Example 1, continued
5. Solve the problem.
Normally, the answer would be rounded down to
46.15. However, when dealing with money, round up
to the nearest whole cent as a retailer would.
x ≤ 46.16
12
• x + 0.04x + 2 ≤ 50
• 1.04x + 2 ≤ 50
• 1.04x ≤ 48
• x ≤ 46.153846
Add like terms.
Subtract 2 from both
sides.
Divide both sides by
1.04.
13. 1.2.2: Creating Linear Inequalities in One Variable
Guided Practice: Example 1, continued
6. Interpret the solution of the inequality in
terms of the context of the problem.
Juan should look for jeans that are priced at or below
$46.16.
13
✔
14. 1.2.2: Creating Linear Inequalities in One Variable
Guided Practice: Example 1, continued
14
15. Guided Practice
Example 2
Alexis is saving to buy a laptop that costs $1,100. So far
she has saved $400. She makes $12 an hour
babysitting. What’s the least number of hours she needs
to work in order to reach her goal?
1.2.2: Creating Linear Inequalities in One Variable
15
16. Guided Practice: Example 1, continued
1. Read the problem statement first.
2. Reread the scenario and identify the known
quantities.
• Needs at least $1,100
• Saved $400
• Makes $12 an hour
3. Read the statement again, identify the unknown
quantity.
Least number of hours Alexis must work to make enough money
1.2.2: Creating Linear Inequalities in One Variable
Alexis is saving to buy a laptop that costs $1,100. So far
she has saved $400. She makes $12 an hour
babysitting. What’s the least number of hours she needs
to work in order to reach her goal?
16
17. 1.2.2: Creating Linear Inequalities in One Variable
Guided Practice: Example 2, continued
4. Create expressions and inequalities from
the known quantities and variable(s).
400 + 12h ≥ 1100
17
Known Unknown
Needs at least $1,100 Least number of hours Alexis
must work to make enough
money
Saved $400
Makes $12 an hour
18. 1.2.2: Creating Linear Inequalities in One Variable
Guided Practice: Example 2, continued
5. Solve the problem.
• 400 + 12h ≥ 1100
Subtract 400 from both sides.
• 12h ≥ 700
Divide both sides by 12.
18
h ³ 58.33
19. 1.2.2: Creating Linear Inequalities in One Variable
Guided Practice: Example 2, continued
6. Interpret the solution of the inequality in
terms of the context of the problem.
In this situation, it makes sense to round up to the
nearest half hour since babysitters usually get paid
by the hour or half hour. Therefore, Alexis needs to
work at least 58.5 hours to make enough money to
save for her laptop.
19
✔
20. 20
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Do you find these slides were useful?
If Yes ,Join Dreams School “Campaign for
Female Education”
Help us in bringing a change in a girl life,
because “When someone takes away your
pens you realize quite how important
education is”.
Just Click on any advertisement on the page,
your one click can make her smile.
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