Properties of Inequalities

Examples, videos, and solutions to help Grade 7 students learn how to justify the properties of inequalities that are denoted by < (less than), ≤ (less than or equal), > (greater than), and ≥ (greater than or equal).

New York State Common Core Math Grade 7, Module 3, Lesson 12

Worksheets for Grade 7

Lesson 12 Student Outcomes

• Students justify the properties of inequalities that are denoted by < (less than), ≤ (less than or equal), > (greater than), and ≥ (greater than or equal).

Lesson 12 Summary

• When both sides of an inequality are added or subtracted by a number, the inequality symbol stays the same and the inequality symbol is said to be preserved.
• When both sides of an inequality are multiplied or divided by a positive number, the inequality symbol stays the same and the inequality symbol is said to be preserved.
• When both sides of an inequality are multiplied or divided by a negative number, the inequality symbol switches from < to > or from > to <. The inequality symbol is reversed.

Classwork

Example 1
Preserves the inequality symbol: means the inequality symbol stays the same.
Reverses the inequality symbol: means the inequality symbol switches less than with greater than and less than or equal to with greater than or equal to.

Station #1: Add or Subtract a Number to Both Sides of the Inequality
Station #2: Multiply each term by -1
Station #3: Multiply or Divide Both Sides of the Inequality by a Positive Number
Station #4: Multiply or Divide Both Sides of the Inequality by a Negative Number

Exercise
Complete the following chart using the given inequality, and determine an operation in which the inequality symbol is preserved and an operation in which the inequality symbol is reversed. Explain why this occurs.

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