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Solving and Graphing Linear Inequalities DIRECTIONS 1. Read the worksheet to see what questions you will have to answer before you continue with this PowerPoint. 2. Read the entire PowerPoint but don’t answer the questions yet. 3. Go through the PowerPoint again and answer the questions. What’s an inequality? Symbols Less than Greater than Less than OR EQUAL TO Greater than OR EQUAL TO NOT equal to Solutions…. A solution set is the set of numbers that satisfy an equation or inequality. The solution set can be show as a graph: -5 -4 -3 -2 -1 0 1 2 3 in words: All real numbers less than 2 or in set notation: {x|x< 2} 4 5 Solutions continued… -5 -4 -3 -2 -1 0 1 2 All real numbers greater than -2 x > -2 3 4 5 Solutions continued…. -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers less than or equal to 1 x 1 Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers greater than or equal to -3 x 3 Did you notice, Some of the dots were solid and some were open? x2 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 x 1 Why do you think that is? If the symbol is > or < then dot is open because it can not be equal. If the symbol is or then the dot is solid, because it can be that point too. Graphing Inequalities Less than: circle shade left Greater than: circle shade right Less than or equal to: dot shade left Greater than or equal to: dot shade right Not equal to: circle shade both directions Solving an Inequality Solving a linear inequality in is much like solving a linear equation. The differences are: 1. You graph the solution set for an inequality. 2. You must flip the inequality sign if you multiply or divide by a negative number. x–3<5 Solve using addition: Add the same number to EACH side. x 3 5 +3 +3 x<8 Solving Using Subtraction Subtract the same number from EACH side. x 6 10 -6 -6 x4 THE TRAP….. When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol to maintain a true statement. Solving using Multiplication Multiply each side by the same positive number. 1 (2) x 3 (2) 2 x6 Solving Using Division Divide each side by the same positive number. 3x 9 3 3 x3 Solving by multiplication of a negative # Multiply each side by the same negative number and REVERSE the inequality symbol. (-1) x 4 (-1) Multiply by (-1). See the switch x 4 Solving by dividing by a negative # Divide each side by the same negative number and reverse the inequality symbol. 2x 6 -2 -2 x3