Name Date Unit 4 Lesson 7 Math 7 Solving Inequalities by Multiplication or Division Today’s Objectives: I can solve and graph one-step inequalities, focusing on multiplication and division. Positive multiplication/division inequalities How to solve: Practice: Solve each inequality and graph the solution on a number line 푒 1. 8푥 ≤ 40 2. > 7 2 푥 3. 4푥 < 40 4. 6 ≥ 7 ℎ 5. 5푥 > 30 6. ≤ 3 4 Negative multiplication/division inequalities: Something VERY STRANGE happens when multiplying or dividing by negatives! Write a true, simple inequality Multiply each side by the same negative number Is the resulting inequality true? Reverse the sign. Now is it true? Write a true, simple inequality Divide each side by the same negative number Is the resulting inequality true? Reverse the sign. Now is it true? When you MULTIPLY or DIVIDE BY a NEGATIVE number, you MUST CHANGE the DIRECTION of the inequality symbol! Practice: Solve each inequality and graph the solution on a number line 푥 1. −2푥 < 10 2. ≥ 4 −3 푘 3. > 9 −2 Make sure you pay attention to which numbers are negatives. ONLY CHANGE the inequality symbol when the COEFFICIENT is NEGATIVE! Do not change if it is POSITIVE! Practice: Solve each inequality, provide a check, and state the solution set. 1. −2푥 < 4 2. 2푥 < −4 3. −3푥 ≤ −6 4. 3푥 ≤ −6 5. Paityn earns $8 per hour working at the zoo. Write and solve an inequality that can be used to find how many hours she must work in a week to earn at least $20. Circle the inequalities in which you’d have to flip the inequality sign: 푥 푥 − 8 < −5 ≥ −3 −3푥 > 15 4 푥 푥 + 3 < −12 −4 > −27 ≥ 9푥 −3 푥 ≥ 25 4푥 ≤ 16 −7푥 > −35 −14 Practice: Write and solve each inequality. 1. A plate weighs ¼ pound. A shelf can hold at most 20 pounds. Write and solve an inequality to find how many plates the shelf can hold. Interpret the solution. 2. Ezra goes to the fair with $25.00. Each ride ticket costs $1.25. Write and solve an inequality to find out how many rides Ezra can ride at the fair. 3. At a baseball game you can get a single hot dog for $2. You have $10 to spend. Write and solve an inequality to find the number of hot dogs you can buy. Interpret the solution. 4. Solve the following inequality and graph the solution set on a number line. Then, provide a check. −3푛 ≤ −22 5. Solve the following inequality and graph the solution set on a number line. Then, provide a check. 푥 < −11 −4 .