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6-1 and 6-2 Solving Inequalities

6-1 and 6-2 Solving Inequalities. Algebra 1 Glencoe McGraw-Hill Linda Stamper. For this lesson you will need a. ruler. and a colored pencil. The graph of an inequality in one variable is the set of points on a number line that represent all solutions of the inequality.

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6-1 and 6-2 Solving Inequalities

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  1. 6-1 and 6-2 Solving Inequalities Algebra 1 Glencoe McGraw-Hill Linda Stamper

  2. For this lesson you will need a ruler and a colored pencil.

  3. The graph of an inequality in one variable is the set of points on a number line that represent allsolutions of the inequality. endpoint 4 • ray O If the endpoint on the graph is not a solution, draw an open dot. If the endpoint on the graph is a solution, draw a solid dot. Then draw an arrowhead to show that the graph continues to infinity. What is the name for the geometric figure that represents the solution?

  4. Graphing an Inequality in One Variable 7> x 1. Write inequality. Rewrite with variable first. x <7 7 2. Draw a line (use arrowheads). • 3. Draw open or solid dot and label the endpoint. 4. Draw the ray in the direction of the inequality symbol. You do NOT need to draw in the tick marks.

  5. A solution of an inequality is a value for the variable that makes the inequality true. You can add or subtract inequalities just like you add or subtract equations. To solve an inequality isolate the variable on one side of the inequality symbol. Follow the basic rule: Whatever you do to one side of the inequality sign, you must also do to the other side of the inequality sign.

  6. Solvex– 6 >–14. Then graph the solution. Write the inequality. Isolate the variable using inverse operations. –8 • Graph.

  7. Solvex– 6 >–14. Then graph the solution. Write the inequality. Isolate the variable using inverse operations. • Graph. –8 How many solutions are there to an inequality problem? Infinite

  8. Solvex– 6 >–14. Then graph the solution. Write the inequality. Isolate the variable using inverse operations. • Graph. –8 The authors of your text use set-builder notation to write the solution. The set of all numbers x such that x is greater than or equal to -8.

  9. Solve. Then graph the solution. Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Write an inequality and then solve. Forty is no greater than the difference of a number and two.

  10. Solve. Then graph the solution. Example 1 58 • Example 2 8 O Did you draw an open dot?

  11. Solve. Then graph the solution. Example 3 26.025 • Example 4 •

  12. Solve. Then graph the solution. Example 5 7 O Ex. 6 Forty is no greater than the difference of a number and two. <

  13. Multiplication and Division Properties of Inequalities If you multiply or divide each side of an inequality by a positive number, the direction of the inequality symbol isunchanged. If you multiply or divide each side of an inequality by a negative number, the direction of the inequality symbol isreversed. /

  14. Solve Write the inequality. Use inverse property. / When you multiply or divide by a negative, reverseinequality symbol. >

  15. Solve. Ex. 7 Ex. 8 Ex. 10 Ex. 9 Write an inequality and then solve. Ex. 11 Negative three eighths times a number is greater than or equal to 12. Find the number. Ex. 12 Two and one half times a number is less than one and one fifth. Find the number.

  16. Solve. Ex. 7 Ex. 8 / > Ex. 10 Ex. 9 / >

  17. Ex. 11 Negative three eighths times a number is greater than or equal to 12. > / < Ex. 12 Two and one half times a number is less than one and one fifth. <

  18. Homework 6-A2 Pages 297 # 20–33, and Pages 305 #17-28.

  19. Inductive Reasoning is making conclusions on patterns you observe. Look for the pattern that results from dividing each side of an inequality by an integer. < < < The inequality symbol reverses direction when you divide by a negative number. > > • • > -6 -8 -10 -12 An inequality symbol points to the smaller number.

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