Unit 4. Day 20.

Today’s Lesson 1) Introduction to inequalities 2) Solving inequalities

𝑥 =7 𝑥 ≤7 Example A: 1 2 3 4 5 6 7 8 9 10 11 -4 -5 -6 -7 -8 -9 -1 -2 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

𝑚 ≥−4 𝑚 =−4 Example B: 1 2 3 4 5 6 7 8 9 10 11 -4 -5 -6 -7 -8 -9 -1 -2 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

𝑥 <6 𝑥 =6 Example C: 1 2 3 4 5 6 7 8 9 10 11 -4 -5 -6 -7 -8 -9 -1 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

𝑛 =−2 𝑛 >−2 Example D: 1 2 3 4 5 6 7 8 9 10 11 -4 -5 -6 -7 -8 -9 -1 1 2 3 4 5 6 7 8 9 10 11 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11

Open Dot: <, > Closed Dot: ≤, ≥

ℎ > −2 𝑗 < −1 𝑘 ≥ 0 𝑚 ≤ 6 Example E: Example F: Example G: Example H:

Example E: ℎ > −2

Example F: 𝑗 < −1

Example G: 𝑘 ≥ 0

Example H: 𝑚 ≤ 6

Is there a short-cut?

Example I: 2 ≤ 𝑛 𝑛 ≥ 2

Today’s Lesson 1) Introduction to inequalities 2) Solving inequalities

A math “sentence” with an equal sign Q: What is an equation? A: A math “sentence” with an equal sign 3𝑥 + 4 = 78 3 5−𝑦 =6−3𝑦 6 𝑎+5 =7−9𝑎 Q: What does it mean to solve an equation? A: To find the value of the variable Q: How do we solve an equation? A: Isolate the variable

Q: What is an inequality? A: A math “sentence” with an inequality 3𝑥 + 4 > 78 3 5−𝑦 ≤6−3𝑦 6 𝑎+5 >7−9𝑎 Q: What does it mean to solve an inequality? A: To find the possible values of the variable Q: How do we solve an inequality? A: Isolate the variable

Example J: 𝑥 + 4 > 7 > −4 −4 𝑥 3

Example K: ≤ 𝑦 − 3 ≤ −5 +3 +3 𝑦 −2

Example L: 3𝑦 − 5 ≤ −4 ≤ +5 +5 3𝑦 1 3 3 𝑦 ≤ 1 3

Example M: 𝑤 4 + 3 >5 > −3 −3 4 𝑤 4 4 2 𝑤>8