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2.8 Solving Inequalities

Learn to solve inequalities following the same steps as equations, including special cases with inequality signs. Understand graphing solution sets with clear examples and tips. Practice problems included.

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2.8 Solving Inequalities

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  1. 2.8 Solving Inequalities

  2. Solving Inequalities • Solving inequalities follows the same procedures as solving equations. • There are a few special things to consider 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 than greater than or equal less 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 left Graph any number greater than or equal to. . . closed circle, line to the right Graph any number less than or equal to. . . closed circle, line to the left

  5. 0 3 Solve the inequality: x + 4 < 7 -4-4 x < 3 • Subtract 4 from each side. • Keep the same inequality sign. • Graph the solution. • Open circle, line to the left.

  6. There is one special case. • Sometimes you may have to reverse the direction of the inequality sign!! • That only happens when you multiply or divide both sides of the inequality by a negative number.

  7. -6 0 Example: • Subtract 5 from each side. • Divide each side by negative 3. • Reverse the inequality sign. • Graph the solution. • Open circle, line to the left. Solve:-3y + 5 >23 -5-5 -3y > 18 -3 -3 y < -6

  8. Try these: • Solve2x+3>x+5 • Solve- c - 11>23 • Solve3(r-2)<2r+4

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