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Mastering Linear Inequalities: Essential Concepts and Strategies

Understand linear inequalities, solve one-step problems, and master graphing solutions with this comprehensive guide. Learn methods for addition, subtraction, multiplication, and division, as well as key principles for maintaining the integrity of inequalities.

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Mastering Linear Inequalities: Essential Concepts and Strategies

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  1. Solving and Graphing Linear Inequalities Solving One-Step Linear Inequalities

  2. What’s an inequality? • Is a range of values, rather than ONE set number • An algebraic relation showing that a quantity is greater than or less than another quantity. Speed limit:

  3. Symbols Less than Greater than Less than OR EQUAL TO Greater than OR EQUAL TO

  4. +3 +3 Solving an Inequality Solving a linear inequality in one variable is much like solving a linear equation in one variable. Get the variable to one side using the opposite operations. Solve using addition: x – 3 < 5 Add the same number to EACH side. x < 8

  5. -6 -6 Solving Using Subtraction Subtract the same number from EACH side.

  6. Using Subtraction… Graph the solution.

  7. Using Addition…

  8. THE TRAP….. When you multiply or divide each side of an inequality by a negative number, you must FLIP the inequality sign to maintain a true statement.

  9. (2) (2) Solving using Multiplication Multiply each side by the same positive number.

  10. 3 3 Solving Using Division Divide each side by the same positive number.

  11. (-1) (-1) See the switch Solving by multiplication of a negative # Multiply each side by the same negative number and REVERSE the inequality symbol. Multiply by (-1).

  12. -2 -2 Solving by dividing by a negative # Divide each side by the same negative number and reverse the inequality symbol.

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