6-1 and 6-2 Solving Inequalities Algebra 1 Glencoe McGraw-HillLinda Stamper

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

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

Graphing an Inequality in One Variable 1. Write inequality. 7 x < 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. 7 > x Rewrite with variable first. You do NOT need to draw in the tick marks.

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.

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

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

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

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

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

Example Solve. Then graph the solution. Example 4

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

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

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

Solve. Ex. 7 Ex. 8 Ex. 9 Ex. 10 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. Write an inequality and then solve.

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

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. < < /

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

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. < < < > > > Inductive Reasoning Inductive Reasoning is making conclusions on patterns you observe. An inequality symbol points to the smaller number.