COMPOUND INEQUALITIES

Compound Inequality

Compound Inequality Two inequalities joined by the word “and” or the word “or”

Compound Inequality Two inequalities joined by the word “and” or the word “or” Example: −5<𝑥<0

Compound Inequality Two inequalities joined by the word “and” or the word “or” Example: −5<𝑥<0 This is read: “- 5 is less than x, and x is less than 0”

Compound Inequality Example: 4≤𝑦≤12

Compound Inequality Example: 4≤𝑦≤12 This is read: “4 is less than or equal to x, and x is less than or equal to 12”

Graphing

Graphing 4≤𝑥<10

Graphing 4≤𝑥<10 To graph, graph the individual inequalities

Graphing 4≤𝑥<10 To graph, graph the individual inequalities 4 10

Graphing 4≤𝑥<10 To graph, graph the individual inequalities 4 10

Graphing 4≤𝑥<10 To graph, graph the individual inequalities 4 10

Graphing 4≤𝑥<10 To graph, graph the individual inequalities 4 10

Graphing 4≤𝑥<10 To graph, graph the individual inequalities 4 10

Graphing 4≤𝑥<10 To graph, graph the individual inequalities 4 10 If the graphed areas will cross, draw one line

Graphing 4≤𝑥<10 To graph, graph the individual inequalities 4 10 If the graphed areas will cross, draw one line 4 10

Writing All real numbers greater than -2, but less than 9

Writing All real numbers greater than -2, but less than 9 Have r stand for the real numbers

Writing All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9

Writing All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9 Graph

Writing All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9 Graph -2 9

Writing All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9 Graph -2 9

Writing All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9 Graph -2 9

Writing All real numbers greater than -2, but less than 9 Have r stand for the real numbers −2<𝑟<9 Graph -2 9

Writing Temperatures from 32oF to 40oF, inclusive.

Writing Temperatures from 32oF to 40oF, inclusive. Inclusive means “to include”

Writing Temperatures from 32oF to 40oF, inclusive. Inclusive means “to include” 32≤𝑡≤40

Solving

Solving −6≤3𝑥<15

Solving −6≤3𝑥<15 Break the compound inequality into the two parts.

Solving −6≤3𝑥<15 Break the compound inequality into the two parts. −6≤3𝑥 3𝑥<15

Solving −6≤3𝑥<15 Break the compound inequality into the two parts. −6≤3𝑥 3𝑥<15 Solve each inequality

Solving −6≤3𝑥<15 Break the compound inequality into the two parts. −6≤3𝑥 3𝑥<15 Solve each inequality −2≤𝑥 𝑥<5

Solving −6≤3𝑥<15 Break the compound inequality into the two parts. −6≤3𝑥 3𝑥<15 Solve each inequality −2≤𝑥 𝑥<5 Combine back into one compound inequality

Solving −6≤3𝑥<15 Break the compound inequality into the two parts. −6≤3𝑥 3𝑥<15 Solve each inequality −2≤𝑥 𝑥<5 Combine back into one compound inequality −2≤𝑥<5

Solving −6≤3𝑥<15 Break the compound inequality into the two parts. −6≤3𝑥 3𝑥<15 Solve each inequality −2≤𝑥 𝑥<5 Combine back into one compound inequality −2≤𝑥<5 Choose a value that fits the inequality statement.

Solving −6≤3𝑥<15 Break the compound inequality into the two parts. −6≤3𝑥 3𝑥<15 Solve each inequality −2≤𝑥 𝑥<5 Combine back into one compound inequality −2≤𝑥<5 Choose a value that fits the inequality statement. The value must work for both sides of the compound inequality.

Solving

Solving −3≤2𝑥−1<7

Solving −3≤2𝑥−1<7 −3≤2𝑥−1

Solving −3≤2𝑥−1<7 −3≤2𝑥−1 −2≤2𝑥

Solving −3≤2𝑥−1<7 −3≤2𝑥−1 −2≤2𝑥 −1≤𝑥

Solving −3≤2𝑥−1<7 −3≤2𝑥−1 2𝑥−1<7 −2≤2𝑥 −1≤𝑥

Solving −3≤2𝑥−1<7 −3≤2𝑥−1 2𝑥−1<7 −2≤2𝑥 2𝑥<8 −1≤𝑥

Solving −3≤2𝑥−1<7 −3≤2𝑥−1 2𝑥−1<7 −2≤2𝑥 2𝑥<8 −1≤𝑥 𝑥<4

Solving −3≤2𝑥−1<7 −3≤2𝑥−1 2𝑥−1<7 −2≤2𝑥 2𝑥<8 −1≤𝑥 𝑥<4 −1≤𝑥<4

Solving 7<−3𝑛+1≤13

Solving 7<−3𝑛+1≤13 7<−3𝑛+1

Solving 7<−3𝑛+1≤13 7<−3𝑛+1 −3𝑛+1≤13

Solving 7<−3𝑛+1≤13 7<−3𝑛+1 −3𝑛+1≤13 6<−3𝑛

Solving 7<−3𝑛+1≤13 7<−3𝑛+1 −3𝑛+1≤13 6<−3𝑛 −2>𝑛

Solving 7<−3𝑛+1≤13 7<−3𝑛+1 −3𝑛+1≤13 6<−3𝑛 −3𝑛≤12 −2>𝑛

Solving 7<−3𝑛+1≤13 7<−3𝑛+1 −3𝑛+1≤13 6<−3𝑛 −3𝑛≤12 𝑛≥−4 −2>𝑛

Solving 7<−3𝑛+1≤13 7<−3𝑛+1 −3𝑛+1≤13 6<−3𝑛 −3𝑛≤12 𝑛≥−4 −2>𝑛 −2>𝑛≥−4

Applications Your test scores in science so far are 83 and 87. What possible grades can you have on your next test to have an average between 85 and 90, inclusive?

Your test scores in science so far are 83 and 87 Your test scores in science so far are 83 and 87. What possible grades can you have on your next test to have an average between 85 and 90, inclusive? 1. What are you trying to find?

Your test scores in science so far are 83 and 87 Your test scores in science so far are 83 and 87. What possible grades can you have on your next test to have an average between 85 and 90, inclusive? 1. What are you trying to find? 2. How do you find an average?

Your test scores in science so far are 83 and 87 Your test scores in science so far are 83 and 87. What possible grades can you have on your next test to have an average between 85 and 90, inclusive? 1. What are you trying to find? 2. How do you find an average? 3. Write your inequality statement.

Your test scores in science so far are 83 and 87 Your test scores in science so far are 83 and 87. What possible grades can you have on your next test to have an average between 85 and 90, inclusive? 1. What are you trying to find? 2. How do you find an average? 3. Write your inequality statement. 85≤ 𝑡+83+87 3 ≤90

85≤ 𝑡+83+87 3 ≤90

85≤ 𝑡+83+87 3 ≤90 85≤ 𝑡+170 3 ≤90

85≤ 𝑡+83+87 3 ≤90 85≤ 𝑡+170 3 ≤90 85≤ 𝑡+170 3 𝑡+170 3 ≤90

85≤ 𝑡+83+87 3 ≤90 85≤ 𝑡+170 3 ≤90 85≤ 𝑡+170 3 𝑡+170 3 ≤90 255≤𝑡+170

85≤ 𝑡+83+87 3 ≤90 85≤ 𝑡+170 3 ≤90 85≤ 𝑡+170 3 𝑡+170 3 ≤90 255≤𝑡+170 85≤𝑡

85≤ 𝑡+83+87 3 ≤90 85≤ 𝑡+170 3 ≤90 85≤ 𝑡+170 3 𝑡+170 3 ≤90 255≤𝑡+170 𝑡+170≤270 85≤𝑡

85≤ 𝑡+83+87 3 ≤90 85≤ 𝑡+170 3 ≤90 85≤ 𝑡+170 3 𝑡+170 3 ≤90 255≤𝑡+170 𝑡+170≤270 85≤𝑡 𝑡≤100

85≤ 𝑡+83+87 3 ≤90 85≤ 𝑡+170 3 ≤90 85≤ 𝑡+170 3 𝑡+170 3 ≤90 255≤𝑡+170 𝑡+170≤270 85≤𝑡 𝑡≤100 85≤𝑡≤100

85≤ 𝑡+83+87 3 ≤90 85≤ 𝑡+170 3 ≤90 85≤ 𝑡+170 3 𝑡+170 3 ≤90 255≤𝑡+170 𝑡+170≤270 85≤𝑡 𝑡≤100 85≤𝑡≤100 So your next test score must be between 85 and 100, inclusive.

Assignment 3.5A: 1 – 19, 47 - 50