Creating & Solving Compound Inequalities · Notes 2.5 Creating & Solving Compound Inequalities...
Transcript of Creating & Solving Compound Inequalities · Notes 2.5 Creating & Solving Compound Inequalities...
Notes2.5
Creating&SolvingCompoundInequalitiesSolvingcompoundinequalitiesinvolving“AND.”Combiningtwoormoresimpleinequalitiesformsacompoundinequality.
Thegraphofacompoundinequalityinvolving“AND”istheintersectionofthetwosimplegraphs.
𝑥 > 2 𝐴𝑁𝐷 𝑥 < 6
4 ≤ 𝑥 + 2 𝐴𝑁𝐷 𝑥 + 2 ≤ 8
4 ≤ 𝑥 + 2 𝐴𝑁𝐷 𝑥 + 2 ≤ 8
4 − 2 ≤ 𝑥 + 2 − 2 𝐴𝑁𝐷 𝑥 + 2 − 2 ≤ 8 − 22 ≤ 𝑥 𝐴𝑁𝐷 𝑥 ≤ 6
2 ≤ 𝑥 ≤ 6
– 5 ≤ 2𝑥 + 3 ≤ 9
– 5 ≤ 2𝑥 + 3 ≤ 9 – 5 ≤ 2𝑥 + 3 𝐴𝑁𝐷 2𝑥 + 3 ≤ 9
– 5 − 3 ≤ 2𝑥 + 3 − 3 𝐴𝑁𝐷 2𝑥 + 3 − 3 ≤ 8 − 3 – 8 ≤ 2𝑥 𝐴𝑁𝐷 2𝑥 ≤ 5−82≤2𝑥2
𝐴𝑁𝐷 2𝑥2≤52
– 4 ≤ 𝑥 ≤ 212
Solvingcompoundinequalitiesinvolving“OR.”Combiningtwoormoresimpleinequalitiesformsacompoundinequality.Thegraphofacompoundinequalityinvolving“OR”istheunionofthetwosimplegraphs.
𝑥 < 2 𝑂𝑅 𝑥 > 6
– 4 + 𝑥 > 1 𝑂𝑅 – 4 + 𝑥 < 3
– 4 + 𝑥 > 1 𝑂𝑅 – 4 + 𝑥 < 3
– 4 + 4 + 𝑥 > 1 + 4 𝑂𝑅 – 4 + 4 + 𝑥 < 3 + 4
𝑥 > 5 𝑂𝑅 𝑥 < 7
2𝑥 ≤ 6 𝑂𝑅 3𝑥 > 15
2𝑥 ≤ 6 𝑂𝑅 3𝑥 > 15 2𝑥2≤62
𝑂𝑅 3𝑥3>153
𝑥 ≤ 3 𝑂𝑅 𝑥 > 5
Youtry:−10 < 3𝑥 + 2 < 8
4𝑥 − 1 < 15 𝑂𝑅 8𝑥 ≥ 48