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Inequalities

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Examples, videos, and solutions to help Grade 7 students understand that an inequality is a statement that one expression is less than (or equal to) or greater than (or equal to) another expression.

New York State Common Core Math Grade 7, Module 3, Lesson 13

Download worksheets for Grade 7, Module 3, Lesson 13

Lesson 13 Student Outcomes

• Students understand that an inequality is a statement that one expression is less than (or equal to) or greater than (or equal to) another expression, such as 2x + 3 < 5 or 3x + 50 ≥ 100.
• Students interpret a solution to an inequality as a number that makes the inequality true when substituted for the variable.
• Students convert arithmetic inequalities into a new inequality with variables (e.g. 2 x 6 + 3 > 12, to 2m + 3 > 12 and give a solution; for example, m = 6, to the new inequality. They check to see if different values of the variable make an inequality true or false.

Lesson 13 Classwork

Opening Exercise: Writing Inequality Statements
Tarik is trying to save $265.49 to buy a new tablet. Right now he has and can save a week from his allowance. Write and evaluate an expression to represent the amount of money saved after: When will Tarik have enough money to buy the tablet?
Write an inequality that will generalize the problem.

Example 1: Evaluating Inequalities—Finding a Solution
The sum of two consecutive odd integers is more than -12. Form true numerical inequality expressions.
Write an inequality that will find all values that will make the inequality true.
The sum of two consecutive odd integers is more than -12. What is the smallest value that will make this true?
a. Write an inequality that can be used to find the smallest value that will make the statement true.
b. Use If-then moves to solve the inequality written in part (a). Identify where the 0's and 1's were made using the If-then moves.




Exercises
1. Connor went to the county fair with a $22.50 in his pocket. He bought a hot dog and drink for $3.75, and then wanted to spend the rest of his money on ride tickets which cost $1.25 each.
a. Write an inequality to represent the total spent where is the number of tickets purchased.
b. Connor wants to use this inequality to determine whether he can purchase 10 tickets. Use substitution to show whether or not he will have enough money.
c. What is the total maximum number of tickets he can buy based upon the given information?

2. Write and solve an inequality statement to represent the following problem:
On a particular airline, checked bags can weigh no more than 50 pounds. Sally packed 32 pounds of clothes and five identical gifts in a suitcase that weigh 8 pounds. Write an inequality to represent this situation.

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