2 1 Writing and Graphing Inequalities Inequalities l

2. 1 Writing and Graphing Inequalities

Inequalities l Mathematical sentences containing <, >, < or > l < is less than l > is greater than l < is less than or equal to l > is greater than or equal to

Writing Inequalities Example 1 A number w minus 3. 5 is less than or equal to w -2. – 3. 5 < -2 b) 3 is less than a number n plus 5. 3 < n + 5 c) Zero is greater than or equal to twice a number x plus one. 0 > 2 x + 1 a)

You try! 1) A number b is fewer than 3. 4. b < 3. 4 2) -7/10 is at least twice a number k minus 4. -7/10 > 2 k - 4

Example 2 l Determine whether each number is a solution to x > 5. a. ) 5 5>5 Yes, 5 is a solution because 5 is equal to 5 b. ) -7 -7 > 5 No, -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 2. ) x > 6 a. ) 6 b. ) -5 c. ) 3 b. ) 0 c. ) 25

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

Example 3 l 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 l Graph ¡ The x > -3 on a number line. 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