Solving Multi-Step Linear Inequalities Practice

Solving a Multi-Step Linear Inequality:

1. Simplify each side separately:
   • Clear parentheses, fractions, and decimals; then combine any like terms
2. Isolate the variable terms on one side:
   • Use the addition property of inequality to get all variable terms on one side and all numbers on the other
3. Isolate the variable:
   • Use the multiplication property of inequality to obtain the form x < k, where < represents any inequality symbol and k is some number

Solving a Three-Part Inequality:

1. 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
2. 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
3. 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: