Day 71 – Solve and Graph one Variable Inequalities

Example 1 Graph the solution of c ≥ ─ 2 on a number line.

Answer Graph the solution of c ≥ ─ 2 on a number line. The solid dot shows that ─ 2 is a solution. The arrow pointing to the right shows that the numbers corresponding to all points to the right of —2 are also solutions. Inequalities can model real world situations.

Example 2 METEOROLOGY Throughout the morning the temperature rent at 5°F. In her noon weather report, the meteorologist stated t hat there had been a sudden change in temperature. a. Write an inequality to describe the temperature t at noon. b. Graph the solution to this inequality on a number line.

Answer METEOROLOGY Throughout the morning the temperature rent at 5°F. In her noon weather report, the meteorologist stated t hat there had been a sudden change in temperature. a. Write an inequality to describe the temperature t at noon. t ≠ 5 the Temperature could be anything except 5°F. b. Graph the solution to this inequality on a number line. The open dot shows that 5 is not a solution. The arrows to -1 0 1 2 the left and to the right show that all real numbers less than 5 and all real numbers greater than 5 are solutions.

Example 3 An advertising agency is interested in knowing the effectiveness of its campaign for Fiesta Foods, Inc., this year. The change in sales since the campaign began may show the effectiveness of the campaign. The annual sales amount for the year before the new campaign was started is shown on this number line.

1. What is the dollar amount of last year's sales. 2 1.What is the dollar amount of last year's sales? 2. Lower annual sales this year than last year may show that the advertising campaign is not very effective. Name an amount less than last year's sales.

3. Name an amount greater than last year's sales. 4 3. Name an amount greater than last year's sales. 4. In Question 2, could you have named other lesser amounts? How many others? Where are the points corresponding to these amounts located on the number line above?

5. In Question 3, could you have named other greater amounts 5. In Question 3, could you have named other greater amounts? How many others? Where are the points corresponding to these amounts located on the number line above? 6. Can you name an amount that is not less than, not greater than, and not equal to last year's sales?