1. 1.6 Solving Inequalities

2. Solving Inequalities ● Solving inequalities follows the same procedures as solving equations. ● There are a few special things to consider with inequalities: ● We need to look carefully at the inequality sign. ● We also need to graph the solution set.

3. Review of Inequality Signs > greater than < less than greater than or equal less than or equal

4. How to graph the solutions > Graph any number greater than... open circle, line to the right < Graph any number less than... open circle, line to the left Graph any number greater than or equal to... closed circle, line to the right Graph any number less than or equal to... closed circle, line to the left

5. Solve the inequality: x + 4 < 7 -4 -4 x < 3 ● Subtract 4 from each side. ● Keep the same inequality sign. ● Graph the solution. Open circle, line to the left. 30

6. There is one special case. ● Sometimes you may have to reverse the direction of the inequality sign!! ● That only happens when you multiply or divide both sides of the inequality by a negative number.

7. Example: Solve: -3y + 5 >23 -5 -5 -3y > 18 -3 -3 y < -6 ● Subtract 5 from each side. ● Divide each side by negative 3. ● Reverse the inequality sign. ● Graph the solution. Open circle, line to the left. 0-6

8. Try these: ● Solve 2x+3>x+5 ● Solve - c - 11>23 ● Solve 3(r-2)<2r+4

9. The product of a number and four is at most −10. Six more than a quotient of a number and three is greater than 14. The width of a rectangle is 4 cm less than the length. The perimeter is at most 48 cm. What are the restrictions on the dimensions of the rectangle? The Morgans are buying a new house. They want to buy either a house more the 75 years old or a house less than 10 years old. Write an inequality representing the situation.

10. Two brothers are saving money to buy tickets to a concert. Their combined savings is $55. One brother has $15 more than the other. How much has each saved? What three consecutive numbers have a sum of 126? Two trains left a station at the same time. One traveled north at a certain speed and the other traveled south at twice that speed. After 4 hours, the trains were 600 miles apart. How fast was each train traveling? You and your friend left a bus terminal at the same time and traveled in opposite directions. Your bus was in heavy traffic and had to travel 20 miles per hour slower than your friend’s bus. After 3 hours, the buses were 270 miles apart. How fast was each bus going?