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Writing and Graphing Inequalities

Writing and Graphing Inequalities. Thumps Up! Do you know these symbols?. < ≤ > ≥. An inequality is a mathematical statement that compares two expressions and includes an inequality symbol . . Writing the Inequality. Write the inequality to represent this phrase: a number less than 5

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Writing and Graphing Inequalities

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  1. Writing and Graphing Inequalities

  2. Thumps Up!Do you know these symbols? • < • ≤ • > • ≥

  3. An inequality is a mathematical statement that compares two expressions and includes an inequality symbol.

  4. Writing the Inequality • Write the inequality to represent this phrase: a number less than 5 • Step 1: Translate the words into an inequality. • Let the variable x represent the unknown number. • Step 2: Explain what the variable, x, represents. • The variable x represents the set of all numbers that are less than 5. • So, 4, 0, and -10 are all possible values of x, because all those numbers are less than 5. • Solution: The phrase “a number less than 5” can be represented as x ˂ 5. The variable, x, represents the set of all numbers that are less than 5.

  5. Unlike equations, which has only one solution, an inequality has many solutions. These solutions are called the solution set. You can use substitution to determine if a value is in the solution set or not.

  6. Graphing the Inequality • Graph an inequality to represent the phrase: a number less than 5 (x < 5) • Step 1: Draw a number line. • Step 2: Draw a circle either open or closed circle on the value from the inequality. • Since x <5, 5 is not a solution. • Draw an open circle around 5. Then shade to the left of 5. • Solution: All values that are less than 5 are part of the solutionset for the inequality x <5.

  7. Example 1 • Todd caught a fish that weighed less than 12 pounds. Write an inequality to represent the situation. • Step 1: Identify and interpret the key words. • Let the variable wrepresent the unknownweight of the fish. • Step 2: Translate the words into an inequality. • Step 3: Graph the inequality. • Since w < 12, 12 is not a solution. • Draw an open circle around 12. Then shade to the left of 12. • Solution: The fish weighs less than 12 pounds, therefore, any number less than 12 is a solution to the situation, but does a negative weight make sense?

  8. Example 2 • Determine if -45, 0, 60 or 75 are solutions to the following inequality: b ≥ 60. Then graph the inequality. • Substitute the given values for b in the inequality. • Determine if the statement for each is true. • -45≥ 60 Is -45 greater than or equal to 60? • 0 ≥ 60 Is 0 greater than or equal to 60? • 60 ≥ 60 Is 60 greater than or equal to 60? • 75 ≥ 60 Is 75 greater than or equal to 60? • 75 and 60 are part of the solution set for b ≥ 60. • Since b ≥ 60, 60 and 75 are solutions because 60and 75 are greaterthan or equal to b. • Draw a closed circle around 60. Then shade to the right of 60. no no yes yes

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