2Solving 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.
3Review of Inequality Signs > greater than< less thangreater than or equalless than or equal
4How 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
5Solve 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
6There 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.
7Example: -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
8Try these:Solve 2x+3>x+5Solve - c - 11>23Solve 3(r-2)<2r+4