3-1 Inequalities and their Graphs

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Presentation transcript:

3-1 Inequalities and their Graphs

An inequality is a mathematical sentence that uses an inequality symbol to compare the values of two expressions Solution of an Inequality: any number that makes the inequality true <𝑳𝒆𝒔𝒔 𝒕𝒉𝒂𝒏 >𝑮𝒓𝒆𝒂𝒕𝒆𝒓 𝒕𝒉𝒂𝒏 ≤𝑳𝒆𝒔𝒔 𝒕𝒉𝒂𝒏 𝒐𝒓 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 ≥𝑮𝒓𝒆𝒂𝒕𝒆𝒓 𝒕𝒉𝒂𝒏 𝒐𝒓 𝒆𝒒𝒖𝒂𝒍 𝒕𝒐 Open Circle Closed Circle

Problem 1: Writing Inequalities What inequality represents the verbal expression? All real numbers x less than or equal to –7

What inequality represents the verbal expression? 6 less than a number k is greater than 13

Problem 2: Identifying Solutions by Evaluating 13−7𝑦≤6 –1 1

Problem 3: Graphing an Inequality What is the graph of 2≥𝑎

What is the graph of 𝑥>−4

What is the graph of 𝑐<0

What is the graph of 3≤𝑛

Problem 4: Writing an Inequality from the Graph What inequality represents the graph?

Problem 4: Writing an Inequality from the Graph What inequality represents the graph?

Problem 5: Writing Real-World Inequalities What inequality describes the situation? Be sure to define a variable.

What inequality describes the situation? Be sure to define a variable.