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6.2: Inequalities with Addition and Subtraction

Difficulty Level: Basic Created by: CK-12
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Suppose your favorite baseball team had wins last year, and this year it vows to win 10 more games. It also promises that the number of its wins this year will be greater than or equal 85. Could you determine how many wins the team had last year? In this Concept, you'll learn to solve inequalities such as the one representing this scenario by using addition and subtraction.

Guidance

Inequalities Using Addition or Subtraction

To solve inequalities, you need some properties.

Addition Property of Inequality: For all real numbers and :

If , then .

If , then .

The two properties above are also true for or .

Because subtraction can also be thought of as “add the opposite,” these properties also work for subtraction situations.

Just like one-step equations, the goal is to isolate the variable, meaning to get the variable alone on one side of the inequality symbol. To do this, you will cancel the operations using inverses.

Example A

Solve for .

Solution: To isolate the variable , you must cancel “subtract 3” using its inverse operation, addition.

Now, check your answer. Choose a number less than 13 and substitute it into your original inequality. If you choose 0, and substitute it you get:

What happens at 13? What happens with numbers greater than 13?

Example B

Solve for .

Solution:

The solution is shown below in a graph:

Example C

Solve for : .

Solution:

Video Review

Guided Practice

Solve for : .

Solution:

Explore More

Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Inequalities Using Addition and Subtraction (7:48)

Solve each inequality and graph the solution on a number line.

Mixed Review

  1. Write an equation containing (3, –6) and (–2, –2).
  2. Simplify: .
  3. Graph on a coordinate plane.
  4. varies directly as . When . Find when .
  5. Rewrite in slope-intercept form: .

Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 6.2. 

Vocabulary

Addition Property of Inequality

Addition Property of Inequality

For all real numbers a, \ b, and c: If x < a, then x + b < a + b. If x < a, then x - c < a - c.

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Difficulty Level:
Basic
Grades:
8 , 9
Date Created:
Feb 24, 2012
Last Modified:
Apr 14, 2016
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