4-3: Solving Inequalities 4-3: Solving Inequalities Using Multiplication and Using Multiplication and DivisionDivisionEssential Question: What is the main difference between solving inequalities and solving equations using multiplication and division.

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷You can multiply the same value

to each side of an inequality, just like you did with equations. ◦When you multiply both sides of an

inequality by a positive number, the direction of the inequality sign stays the same

◦When you multiply both sides of an inequality by a negative number, reverse the sign of the inequality.

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷Example 1: Multiplying by a

positiveSolve x/2 < -1. Graph the solution.

◦x/2 < -1

◦●2 ●2 Multiply each side by 2

◦x < -20 1 2 3 4 50–1–2–3–4–5

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷Your Turn

◦Solve b/4 > ½. Graph your solution. b > 2

◦Solve d/3 > 5/6. Graph your solution. d > 2 ½

0 1 2 3 4 50–1–2–3–4–5

0 1 2 3 4 50–1–2–3–4–5

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷Example 2: Multiplying by a

negativeSolve -k/4 > -1. Graph the

solution.◦-k/4 > -1

◦●-4 ●-4 Multiply each side by -4

◦k < 4 Flip the inequality

0 1 2 3 4 50–1–2–3–4–5

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷Your Turn

◦Solve -6 > -1/5 w. Graph your solution. 30 < w

22 23 24 25 26 27 28 29 30 31 32 33 34

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷Solving inequalities is similar to

solving with multiplication. If you divide by a negative number, flip the inequality.

Example 1: Solve -5z > 25. Graph the solution.◦-5z > 25◦÷-5 ÷-5 Divide each side

by -5◦z < -5 Flip the inequality

0 1 2 3 4 50–1–2–3–4–5

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷Your Turn

◦Solve -2t < -8. Graph your solution. t > 4

◦Solve -3w > 12. Graph your solution. w < -4

0 1 2 3 4 50–1–2–3–4–5

0 1 2 3 4 50–1–2–3–4–5

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷Example 4: Real-World Application

◦The student council votes to buy food for a local food bank. A case of 12 jars of spaghetti sauce costs $13.75. What is the greatest number of cases of sauce the students can buy if they use at most $216 for this project? Let c = the number of cases of sauce 13.75c < 216 ÷13.75 ÷13.75 c < 15.71

◦At most, they can buy 15 cases (they don’t have enough money to buy 16 cases)

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷Your Turn

◦Students in the school band are selling calendars. They earn $0.40 on each calendar they sell. Their goal is to earn more than $327. Write and solve an inequality to find the number of calendars they can sell and still reach their goal. 0.40c > 327 c > 817.5 They need to sell at least 818 calendars

4-3: Inequalities Using 4-3: Inequalities Using ● ● & ÷& ÷Assignment

◦Worksheet 4-3◦1 – 45, odd problems