Algebra 3.4 & 3.5 3.4 Solving Two-Step and Multistep Inequalities 3.5 Solving Inequalities with Variables on Both Sides.

Learning Targets Language Goal Students will be able to read inequalities that have more than one operation. Math Goal Students will be able to solve inequalities that have more than one operation. Essential Question How are solutions to inequalities different from solutions of equations?

Warm-up

Homework Check

Homework Check

3.1 – 3.3 Review Graphing Inequalities 1. 4 > x + 2 2. 2x < -2

3.1 – 3.3 Review Define a variable and write an inequality for each situation. Graph the solutions. There must be at least 11 players in order to play the soccer game. A trainer advises an athlete to keep his heart rate under 140 beats per minute.

3.1 – 3.3 Review Write the inequality shown by each graph. 5 6 7 -3 -2 -1

3.1 – 3.3 Review Solve the inequality. 𝑥 −2 ≤5 2. 𝑥−2<−8 𝑥 −2 ≤5 2. 𝑥−2<−8 3. 6𝑥≥−36 4. 𝑥 + 9 >15

3.4 Example 1 Solving Multi-step Inequalities 1. 160+4𝑓≤500 2. 7−2𝑡≤21

3.4 Example 1 Solving Multi-step Inequalities Solve and graph the solution 3. 𝑥+5 −2 >3 4. 1−2𝑛 3 ≥7

3.4 Example 2 Simplify before solving Inequalities Solve and graph the solution 1. −4+ −8 <−5𝑐−2 2. −3 3−x < 4 2

3.4 Example 2 Simplify before solving Inequalities Solve and graph the solution 3. 4 5 𝑥+ 1 2 > 3 5 4. 3+2 𝑥+4 >3

3.5 Notes Example 1 Solving Inequalities with Variables on Both Sides Solve each inequality and graph the solution. 1. 𝑥 < 3𝑥 + 8 2. 6𝑥 – 1≤3.5𝑥+4

3.5 Notes Example 1 Solving Inequalities with Variables on Both Sides Solve each inequality and graph the solution. 3. 𝑦≤4𝑦+18 4. 4𝑚 −3<2𝑚+6

3.5 Notes Example 1 Solving Inequalities with Variables on Both Sides Solve each inequality and graph the solution. 5. 4𝑥≥7𝑥+6 6. 5𝑡+1<−2𝑡−6

3.5 Notes Example 2 Word Problems Set up an inequality and solve. 1. A-Plus advertising charges a fee of $24 plus $0.10 per flyer to print and deliver flyers. Print and more charges $0.25 per flyer. For how many flyers is the cost at A-Plus Advertising less than the cost at Print and More?

3.5 Notes Example 2 Word Problems Set up an inequality and solve. 2. The Home Cleaning Company charges $312 to power-wash the siding of a house plus $12 for each window. Power Clean charges $36 per window, and the price includes power-washing the siding. How many windows must a house have to make a total cost from The Home Cleaning Company less expensive than Power Clean?

3.5 Example 3 Simplifying each Side Before Solving Solve each inequality and graph the solution. 1. 6(1 – 𝑥)<3𝑥 2. −0.2𝑥 + 0.9≥1.6𝑥

3.5 Example 3 Simplifying each Side Before Solving 3. 5(2−𝑟)≥3(𝑟−2) Solve each inequality and graph the solution. 3. 5(2−𝑟)≥3(𝑟−2) 4. 0.5x −0.3+1.9x<0.3x+6

3.5 Example 3 Simplifying each Side Before Solving 5. 2 𝑘−3 >6+3𝑘−3 Solve each inequality and graph the solution. 5. 2 𝑘−3 >6+3𝑘−3 6. 4m−3<2m+6

Review Vocabulary Identity Contradiction When solving an inequality, if you get a statement that is always true, the original inequality is an identity, and all real numbers are solutions. Example: 1 < 7 When solving an inequality, if you get a false statement, the original inequality is a contradiction, and has no solutions. Example: 7 < 0

3.5 Example 4 Solve each inequality 1. 𝑥+5≥𝑥+3 2. 2𝑥+6<5+2𝑥 State whether it is an identity or contradiction 1. 𝑥+5≥𝑥+3 2. 2𝑥+6<5+2𝑥

3.5 Example 4 Solve each inequality 3. 2𝑥−7≤5+2𝑥 4. 2 3𝑦−2 −4≥3(2𝑦+7) State whether it is an identity or contradiction 3. 2𝑥−7≤5+2𝑥 4. 2 3𝑦−2 −4≥3(2𝑦+7)

3.5 Example 4 Solve each inequality 5. 4 𝑦−1 ≥4𝑦+2 6. 𝑥−2<𝑥+1 State whether it is an identity or contradiction 5. 4 𝑦−1 ≥4𝑦+2 6. 𝑥−2<𝑥+1

Whiteboards #1 5𝑥−2 6−5𝑥 >18

Whiteboards #2 0<5 7−𝑥 +12𝑥

Whiteboards #3 3 𝑥+4 −5(𝑥−1)≤5

Whiteboards #4 4 2𝑥−3 +2(𝑥+4)≥66

Whiteboards #5 4𝑥−54=−5𝑥

Whiteboards #6 4𝑥−3=3 𝑥+2 −5

Whiteboards #7 0<4 6−𝑥 +7𝑥

Whiteboards #8 6 𝑥+2 −4𝑥≤48

Whiteboards #9 7(2−𝑥)≥3(𝑥+8)

Whiteboards #10 5 𝑥+3 −2𝑥≥−21

Lesson Quiz 3.4

Lesson Quiz 3.5