# 3-6 Compound Inequalities

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3-6 Compound Inequalities

Compound Inequality: Consists of two distinct inequalities joined by the word and or the word or

πβ€πβ€π

Problem 1: Writing Compound Inequality
What compound inequality represents the phrase? Graph the solutions. All real numbers that are greater than β2 and less than 6

What compound inequality represents the phrase. Graph the solutions
What compound inequality represents the phrase? Graph the solutions. All real numbers that are less than 0 or greater than or equal to 5

Problem 2: Solving a Compound Inequality Involving And
What are the solutions of β3β€πβ4<β1? Graph the solutions.

What are the solutions of β2<3π¦β4<14? Graph the solutions.

Problem 4: Solving Compound Inequality Involving OR
What are the solutions of 3π‘+2<β7 ππ β4π‘+5<1 Graph Solutions

What are the solutions of β2π¦+7<1 ππ 4π¦+3β€β5 Graph Solutions

Interval Notation: includes the use of three special symbols Parentheses: Use ( or ) when a < or > symbol indicates that the intervalβs endpoints are NOT included Brackets: Use [ or ] when a β€orβ₯ symbol indicates that the intervalβs endpoints ARE included Infinity: Use β when the interval continues forever in the POSITIVE direction. Use ββ when the interval continues forever in a NEGATIVE direction

Examples of what Interval notation would look like
Found on Page 203

Problem 5: Using Interval Notation
What is the graph of β4, 6 How do you write [β4, 6) as an inequality?

What is the graph of π₯β€β1 ππ π₯>2?
How do you write π₯β€β1 ππ π₯>2 in interval notation