Transcript Writing Inequalities from Word Problems

Lesson 2.3
Creating Inequalities from Word
Problems
<, >, ≤, ≥, ≠
Concept: Solving Inequalities in One Variable
EQ: How do I create inequalities from word problems?
(Standard: CED.1)
Vocabulary: Inequality, Less than, Less than or
equal to, More than, More than or equal to, No more
than, No fewer than
Vocabulary
• Inequality: mathematical sentences that are
similar to equations but 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.
• Less Than: <
• Less than or equal to: ≤
• More Than: >
• More than or equal to: ≥
• No More Than: ≤
Key Concepts
Symbol
Description
Example
Solution
>
greater than,
more than,
over, above
x>3
all numbers greater than 3;
doesn’t include 3
≥
greater than or
equal to, at
least, no less
than, minimum
x≥3
all numbers greater than or
equal to 3; includes 3
<
less than, fewer
than, below,
under
x<3
all numbers less than 3;
does not include 3
≤
less than or
equal to, no
more than, at
most, maximum
x≤3
all numbers less than or
equal to 3; includes 3
≠
not equal to
x≠3
includes all numbers except 3
Other Key Concepts… Notice how
familiar this is.
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.
Group Examples
Create an expression to represent each of the
following:
1. A number and 20 can be no more than 41
2. Four times some number is at most 16
3. The minimum value of a number is 84
4. 45 is more than a number
Getting into longer word problems…
http://www.virtualnerd.com/algebra1/algebra-foundations/real-number-representcompare/inequalities-real-numbercompare/solve-inequality-from-word-problem
Example 1
Susan is saving for a house. She needs at least
$2,000 for her down payment. She makes $15
an hour. Write an inequality to represent the
minimum number of hours she can work to
afford the down payment.
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. Write an inequality
to represent the least number of hours she has to
work to buy the laptop.
You Try!
The elevator can hold a maximum of 2,500
pounds. If 5 people get on the elevator together
and they all weigh the same amount, write an
inequality to represent the most each of them
can weigh to be on the elevator.
Example 3
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, write an inequality to
represent the highest priced jeans he can afford.
Example 4
The students at Dayton High School are
selling candles and scented soaps to raise
money for a new computer lab. They will earn
$10 for every candle they sell. They need to
raise a minimum of $2,020 to have enough
money to finish construction of the computer
lab. Write an inequality to represent the least
number of candles they must sell.