Related Topics:

Lesson Plans and Worksheets for Grade 7

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 7

Common Core For Grade 7

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

Download worksheets for Grade 7, Module 3, Lesson 12

### Lesson 12 Student Outcomes

### 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.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Lesson Plans and Worksheets for Grade 7

Lesson Plans and Worksheets for all Grades

More Lessons for Grade 7

Common Core For Grade 7

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).

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

• 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.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.