ALGEBRA READINESS LESSON 9-3 Warm Up Lesson 9-3 Warm-Up

ALGEBRA READINESS LESSON 9-3 Warm Up Lesson 9-3 Warm-Up

ALGEBRA READINESS “Solving Inequalities by Dividing” (9-3) (3-1) What is the “Division Property of Inequality”? Rule: Division Property of Inequality: If you divide both sides of an inequality by the same number, the inequality is equivalent to the original inequality. if a > b, then a  c > b  c if a < b, then a  c < b  c Example: 4 > 2, so 4  2 > 2  2 Example: 6 < 10, so 6  2 < 10  2 2 > 1 3 < 5 Note: This property is also true for ≥ and ≤ Rule: Division Property of Inequality when c < 0: If you divide both sides of an inequality by a negative number, the inequality sign must be reversed (switched around). if a > b, then a  -c b  -c Example: 4 > 2, but 4   Note: This property is also true for ≥ and ≤.

ALGEBRA READINESS Solve – 5b ≤ 15. – 5b ≤ 15. Use the Division Property of Inequality to isolate the variable. Reverse the direction of the inequality symbol. – 5b – 5 15 – 5 ≥ Simplify. b ≥ – 3. Solving Inequalities by Dividing LESSON 9-3 Additional Examples

ALGEBRA READINESS A woodworker makes a profit of $30 on each picture frame sold. How many frames must she sell to make a profit of at least $500? Words $30 times number of is at least $500 frames sold f Let f = the number of frames. Inequality 30 f ≥ f ≥ 500 Simplify. f ≥ It is not possible to sell two-thirds of a frame, so the woodworker must sell at least 17 frames. Isolate the variable. Use the Division Property of Inequality. 30f > Solving Inequalities by Dividing LESSON 9-3 Additional Examples

ALGEBRA READINESS Solve –4c < 24. Graph the solution. c > –6Simplify. Divide each side by –4. Reverse the inequality symbol. –4c –4 > 24 –4 Solving Inequalities by Dividing LESSON 9-3 Additional Examples

ALGEBRA READINESS Your family budgets $160 to spend on fuel for a trip. How many times can they fill the car’s gas tank if it cost $25 each time? Your family can fill the car’s tank at most 6 times. cost per total fuel tankbudget Words:times number of tanks is at most Define:Let = the number of tanks of gas. t Equation: t < 25t 160 < t 6.4Simplify. < Divide each side by 25. < 25t Solving Inequalities by Dividing LESSON 9-3 Additional Examples

ALGEBRA READINESS Solve each inequality. 1.9c ≤ – 362. – 7r ≥ 14 3.Leroy’s class is having a cookie sale to raise money for a class trip. They will sell homemade cookies for $1.50 each. If they earn at least $200, a local business will match the amount they earn. At least how many cookies do they need to sell to get the local company to match their cookie-sale earnings? c ≤ – cookies r ≤ – 2 Solving Inequalities by Dividing LESSON 9-3 Lesson Quiz