4-1 to 4-3 One-Step Inequalities

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Presentation transcript:

4-1 to 4-3 One-Step Inequalities

Symbols < means “less than” > means “greater than” < means “less than or equal to” > means “greater than or equal to”

Graphing Inequalities To graph an inequality: Draw a number line with “0” and the important number(s). Put an open circle at the important number. Decide if it stays open or is colored in. Shade in the proper direction. Graph X < 3 3

Graphing Inequalities To graph an inequality: Draw a number line with “0” and the important number(s). Put an open circle at the important number. Decide if it stays open or is colored in. Shade in the proper direction. Graph X > 3 3

Graphing Inequalities To graph an inequality: Draw a number line with “0” and the important number(s). Put an open circle at the important number. Decide if it stays open or is colored in. Shade in the proper direction. Graph X > 3 3

Is it a Solution? Is 3 a solution of 2x - 5 > 4? 2·3 – 5 = 1. No, not a solution.

Addition Property of Inequality If a > b, then a + c > b + c for every real number a, b and c.

Subtraction Property of Inequality If a > b, then a - c > b - c for every real number a, b and c.

Treat inequalities just like equations. Solve: x – 2 < -1 +2 +2 How to Solve Treat inequalities just like equations. Solve: x – 2 < -1 +2 +2

Treat inequalities just like equations. Solve: x – 2 < -1 +2 +2 How to Solve Treat inequalities just like equations. Solve: x – 2 < -1 +2 +2

How to Solve Treat inequalities just like equations. Solve: x – 2 < -1 +2 +2 x < 1 1

Multiplication Property of Inequality If a > b, then a · c > b · c if c > 0 a · c < b · c if c < 0

The “Real” Rule If you multiply or divide BY a negative number, then you have to switch the inequality sign.

Treat inequalities just like equations. Solve: -2x < -1 -2 -2 How to Solve Treat inequalities just like equations. Solve: -2x < -1 -2 -2

How to Solve Treat inequalities just like equations. Solve: -2x < -1 -2 -2 x > 1/2

Today’s Assignment P. 202 #4-48 multiples of 4 P. 215 #1-27 odds DUE AT END OF HOUR! (even if you are not done, we will work some more on it on Monday)