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# A16-1 One-Step Linear Inequalities

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### A16-1 One-Step Linear Inequalities

1. 1. Inequalities Algebra 2 6.1 p. 334
2. 2. <ul><li>For each part, check to see if the inequality sign is still facing the right direction. </li></ul>
3. 3. Graphing Linear Inequalities <ul><li>All real numbers less than 2: </li></ul><ul><li>x < 2 </li></ul>0
4. 4. Graphing Linear Inequalities <ul><li>All real numbers greater than -2: </li></ul><ul><li>x > -2 </li></ul>0
5. 5. Graphing Linear Inequalities <ul><li>All real numbers less than or equal to 1: </li></ul><ul><li>x  1 </li></ul>0
6. 6. Graphing Linear Inequalities <ul><li>Real numbers greater than or equal to 0: </li></ul><ul><li>x  0 </li></ul>0
7. 7. Graphing Linear Inequalities <ul><li>An open dot is used for < or > and a solid dot for  or  . </li></ul>
8. 8. Example 1 <ul><li>Average speed = distance </li></ul><ul><li> time </li></ul><ul><li>A faster runner’s average speed must be greater than Sue’s average speed. </li></ul>
9. 9. Example 1 <ul><li>Since the problem asks for all the runners faster than Sue, we will represent that with a variable (like x). </li></ul>
10. 10. Example 1 <ul><li>Since the problem asks for all the runners faster than Sue, we will represent that with a variable (like x). </li></ul><ul><li>Faster average speed = x </li></ul><ul><li>Distance = 2 miles </li></ul><ul><li>Sue’s time = 10 minutes </li></ul>
11. 11. Example 1 <ul><li>Faster average speed > distance </li></ul><ul><li> Sue’s time </li></ul><ul><li>x > 2 / 8 </li></ul>
12. 12. Solving Inequalities <ul><li>You solve linear inequalities the same way you solve equations. </li></ul><ul><li>The only difference is that you HAVE TO flip the inequality sign when multiplying or dividing by a negative number . </li></ul>
13. 13. Solving Inequalities <ul><li>Reverse addition and subtraction </li></ul>
14. 14. Solving Inequalities <ul><li>Reverse addition and subtraction </li></ul><ul><li>Reverse multiplication and division </li></ul>
15. 15. Solving Inequalities <ul><li>Reverse addition and subtraction </li></ul><ul><li>Reverse multiplication and division </li></ul><ul><li>Reverse exponents </li></ul>
16. 16. Solving Inequalities <ul><li>Reverse addition and subtraction </li></ul><ul><li>Reverse multiplication and division </li></ul><ul><li>Reverse exponents </li></ul><ul><li>Reverse parentheses </li></ul>