2.1 Inequalities and Their Graphs CA 1.0 Use arithmetic properties of integers

Inequalities Mathematical sentences containing,

Writing Inequalities Example 1 a)A number w minus 3.5 is less than or equal to -2. b)3 is less than a number n plus 5. c)Zero is greater than or equal to twice a number x plus one. w – 3.5 < -2 3 < n > 2x + 1

You try! 1) A number b is fewer than ) -7/10 is at least twice a number k minus 4. b < /10 > 2k - 4

Example 2 Determine whether each number is a solution to x > 5. a.) 5 5 > 5Yes, 5 is a solution because 5 is equal to 5 b.) > 5No, -7 is not a solution because it is not greater than 5

You try! Determine whether the given number is a solution to the inequality. 1.) x < 3 a.) 15 b.) -5c.) 3 2.) x > 6 a.) 6b.) 0c.) 25

Graphing Inequalities A graph of an inequality with one variable is on a number line. are graphed using an open point since that number is not included as a solution. are graphed using a closed point since that number is included as a solution.

Example 3 Graph x < 2 on a number line.  The solutions of x < 2 are all number less than 2. They are shown by shading all numbers to the left of 2 on a number line.

Example 4 Graph x > -3 on a number line.  The solutions of x > -3 are -3 and all points to the right of -3.

You try! Graph x < 8 on a number line.

Example 5 Write an inequality that represents the graph. x > -3

You try! Write an inequality that represents the graph. x < 4