Algebra I Recipe: Solving Inequalities With One Variable

A. Inequality Symbols

1. > represents "is greater than"
2. < represents "is less than"
3. ≥ represents "is greater than or equal to"
4. ≤ represents "is less than or equal to"

B. Steps for Solving Inequalities with One Variable

1. Perform the distributive property on each side.
2. Combine like terms on each side.
3. Add or subtract to get the variable terms on the same side. (Side of the largest coefficient.)
4. Add or subtract to move the number term to the opposite side of the variable term.
5. Multiply or divide to move the coefficient.
   • If you multiply or divide both sides of an inequality by a negative number, the inequality symbol changes directions.

C. Steps for Graphing the Solutions to Inequalities with One Variable
      ** Make sure the variable is on the LEFT in all solutions.

1. A solution with >
• Graph an open circle on the number. (The number is not part of the solution.)
• A darkened bar with an arrow goes to the right of the circle.
2. A solution with <
• Graph an open circle on the number. (The number is not part of the solution.)
• A darkened bar with an arrow goes to the left of the circle.
3. A solution with ≥
• Graph a solid circle on the number. (The number is part of the solution.)
• A darkened bar with an arrow goes to the right of the circle.
4. A solution with ≤
• Graph a solid circle on the number. (The number is part of the solution.)
• A darkened bar with an arrow goes to the left of the circle.
5. A solution with a fraction.
• Determine the two integers that the fraction falls between.
• Use these two integers to make one big unit on the number line.
• Divide this unit into the appropriate fractional parts like 1/4's, 1/2's, 1/3's, etc.
• Then graph using Steps 1-4 given above.
6. A solution with a decimal.
• Change the decimal to a fraction and graph using Step 5.

Practice Problems