Practice Objectives

- Demonstrate an understanding of the addition property of inequality
- Demonstrate an understanding of the multiplication property of inequality
- Demonstrate the ability to solve a multi-step linear inequality in one variable
- Demonstrate the ability to solve a three-part linear inequality in one variable

## Practice Solving Three-Part Inequalities

Instructions:

Answer 7/10 questions correctly to pass.

Solve each inequality.

Problem:

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Solving a Three-Part Inequality:

- Simplify the middle part (the expression with the variable):
- Clear parentheses if needed and combine any like terms within the middle expression
- Clear any fractions by multiplying each part by the LCD of all denominators
- Clear any decimals by multiplying each part by the appropriate power of 10

- Isolate the variable term in the middle:
- Use the addition property of inequality to get the variable term alone in the middle
- For a three-part inequality, this means adding the same number to each part

- Isolate the variable in the middle:
- Use the multiplication property of inequality to obtain the form a < x < b, where < could also be ≤
- When multiplying or dividing both sides by a negative number, we must flip the direction of all inequality symbols; Ensure that we write our numbers in the order of the number line

Step-by-Step:

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