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# 1.5 Solving Inequalities

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• ### 1.5 Solving Inequalities

1. 1. 1.5 SOLVING INEQUALITIES
2. 2. INEQUALITIES <ul><li>An inequality is a relationship in which two quantities may not be equal. </li></ul><ul><ul><li>Phrases such as “at most” and “at least” suggest this type of relationship </li></ul></ul>
3. 4. WRITE THE INEQUALITY THAT REPRESENTS THE SENTENCE. <ul><li>5 fewer than a number is at least 12 </li></ul><ul><li>The product of a number and 8 is greater than 25 </li></ul>
4. 5. SOLVING INEQUALITIES <ul><li>The solutions of an inequality are the numbers (values) that make it true. </li></ul><ul><li>We solve inequalities the same way we solve equations </li></ul><ul><ul><li>Except: when we multiply or divide by a negative number , we reverse the inequality symbol </li></ul></ul>
5. 6. SOLVE EACH INEQUALITY. GRAPH THE SOLUTION.
6. 7. SOLVE EACH INEQUALITY. GRAPH THE SOLUTION.
7. 8. SOLVE EACH INEQUALITY. GRAPH THE SOLUTION.
8. 9. SOLVE EACH INEQUALITY. GRAPH THE SOLUTION.
9. 10. NO SOLUTION OR ALL REAL NUMBERS AS SOLUTIONS <ul><li>When solving inequalities, we can reach solutions that seem strange and require analysis. </li></ul><ul><ul><li>If we reach a false statement , there are no solutions , and the statement is never true </li></ul></ul><ul><ul><li>If the variable(s) drop out and we have a true statement or we reach a point where one side is identical to the other, the statement is always true for all real numbers . </li></ul></ul>
10. 11. IS THE INEQUALITY ALWAYS, SOMETIMES, OR NEVER TRUE?
11. 12. IS THE INEQUALITY ALWAYS, SOMETIMES, OR NEVER TRUE?
12. 13. IS THE INEQUALITY ALWAYS, SOMETIMES, OR NEVER TRUE?
13. 14. COMPOUND INEQUALITIES <ul><li>A compound inequality is an inequality statement that joins two inequalities using the word and or the word or . </li></ul>
14. 15. COMPOUND INEQUALITIES <ul><li>To solve a compound inequality containing and : </li></ul><ul><ul><li>Find all values of the variable that make both inequalities true </li></ul></ul>
15. 16. SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.
16. 17. COMPOUND INEQUALITIES <ul><li>To solve a compound inequality containing or : </li></ul><ul><ul><li>Find all values of the variable that make at least one of the inequalities true. </li></ul></ul>
17. 18. SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.
18. 19. SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.
19. 20. SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.
20. 21. SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.