2 Solving InequalitiesSolving inequalities follows the same procedures as solving equations.There are a few special things toconsider with inequalities:We need to look carefully at the inequality sign.We also need to graph the solution set.
3 Review of Inequality Signs > greater than< less thangreater than or equalless than or equal
4 How to graph the solutions > Graph any number greater than. . .open circle, line to the right< Graph any number less than. . .open circle, line to the leftGraph any number greater than or equal to. . .closed circle, line to the rightGraph any number less than or equal to. . .closed circle, line to the left
5 Solve the inequality: -4 -4 x < 3 x + 4 < 7 x < 3Subtract 4 from each side.Keep the same inequality sign.Graph the solution.Open circle, line to the left.3
6 There is one special case. Sometimes you may have to reverse the direction of the inequality sign!!That only happens when youmultiply or divide both sides of the inequality by a negative number.
7 Example: -3y > 18 Solve: -3y + 5 >23 -5 -5 -3y > 18y < -6Subtract 5 from each side.Divide each side by negative 3.Reverse the inequality sign.Graph the solution.Open circle, line to the left.-6
8 Try these:Solve 2x+3>x+5Solve - c - 11>23Solve 3(r-2)<2r+4