3 1 Graphing and Writing Inequalities Objectives Identify

3. 1 Graphing and Writing Inequalities

Objectives Identify Solutions of inequalities in one variable Write and graph inequalities in one variable

Words to Know An inequality is a statement that two quantities are not equal. The quantities are compared by using the following signs: < A<B A is less than B. > ≤ ≥ A>B A≤B A≥B A≠B A is greater than B. A is less than or equal to B. A is greater than or equal to B. A is not equal to B. ≠

How do we graph Inequalities?

Graphing Inequalities Verbal Phrase All real numbers is less than 2 Inequality x<2 Graph -4 -2 0 2 4

Graphing Inequalities Verbal Phrase All real numbers is less than or equal to -1 Inequality x < -1 Graph -4 -2 0 2 4

Translate each sentence below 1) Five more than x is greater than or equal to 19. 2) Sixteen less than is less than 4 less y. x + 5 ≥y 19 3) Eleven is lessythan to the quotient of m - 16 <or 4 -equal y and 8. 11 ≤one m ÷ more 8 4) Seven is at least than twice x. 7 > 2 x + 1

Match the inequality with its graph 1. x > -2 A 2. x < -1 B 3. 0>x C 4. 4>x D -4 -2 0 2 4

Ray’s dad told him not to turn on the air conditioner unless the temperature is at least 85°F. Define a variable and write an inequality for the temperatures at which Ray can turn on the air conditioner. Graph the solutions. Let t represent the temperatures at which Ray can turn on the air conditioner. Turn on the AC when temperature is at least 85°F t t 85 70 75 80 85 90 85 ≥ Draw a solid circle at 85. Shade all numbers greater than 85 and draw an arrow pointing to the right.

Lesson Quiz: Part I 1. Describe the solutions of 7 < x + 4. all real numbers greater than 3 2. Graph h ≥ – 4. 75 – 4. 5 Write the inequality shown by each graph. 3. 4. x≥ 3 x < – 5. 5

Lesson Quiz: Part II 5. A cell phone plan offers free minutes for no more than 250 minutes per month. Define a variable and write an inequality for the possible number of free minutes. Graph the solution. Let m = number of minutes. 0 ≤ m ≤ 250 0 250