1. 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

2. 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: ≤

3. 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

4. Other Key Concepts… Notice how familiar this is.
Creating Inequalities from Context
Read the problem statement first.
Reread the scenario and make a list or a table of the known quantities.
Read the statement again, identifying the unknown quantity or variable.
Create expressions and inequalities from the known quantities and variable(s).
Solve the problem.
Interpret the solution of the inequality in terms of the context of the problem.

5. Create an expression to represent each of the following:
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

6. Getting into longer word problems…

7. 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.

8. 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.

9. 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.

10. 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.

11. 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.