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Inequalities

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Types of Number Sentences Equations are number sentences in which two expressions are related using an equal sign. Equations are number sentences in which two expressions are related using an equal sign.

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Types of Number Sentences Inequalities are number sentences that state that one expression is not equivalent to another expression. Inequalities are number sentences that state that one expression is not equivalent to another expression.

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Symbols used in Inequalities < means less than > means greater than means less than or equal to means less than or equal to means greater than or equal to means greater than or equal to means not equal to means not equal to means approximately means approximately

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9 > 5 nine is greater than five 9 > 5 nine is greater than five x 10 x is less than or equal to ten x 10 x is less than or equal to ten x 6 x is not equal to 6 x 6 x is not equal to 6 X 8 x is greater than or equal to 8 X 8 x is greater than or equal to 8 12 < 15 twelve is less than fifteen 12 < 15 twelve is less than fifteen

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Graphing on a number line X = 2 ½ X = 2 ½ Place a closed circle on the number line.

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Graphing on a number line x 2 ½ Place an open circle on the number line and shade both to the left and to the right.

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Graphing on a Number line x < 2 ½ Place an open circle on the number line and shade the line to the left.

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Graphing on a Number line Place an open circle on the number line and shade the line to the right. x > 2 ½

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Graphing on a Number line X 2 ½ X 2 ½ Place a closed circle on the number line and shade the line to the left.

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Graphing on a Number line x 2 ½ x 2 ½ Place a closed circle on the number line and shade the line to the right.

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Graphing Inequalities

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Vocabulary < > Less than Greater than At most At least Fewer than More than No more than No less than UnderOverMaximumMinimum BelowAbove

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Translating increased A. Three times a number increased by 4 is at least 16. B. Five less than a number is at most 11. C.The sum of a number and 7 is less than 19. D. Ellen spent more than $15 at the amusement park. E. Greg plans to spend no more than $48 for shoes. G 48 F. Linda plans to spend at most $85 on jeans and shirts. J + S 85 + 3x + 4 16 > E > 15 – x – 5 11 + x + 7 < 19

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Translating E. Greg plans to spend no more than $48 for shoes. F. Linda plans to spend at most $85 on jeans and shirts. G 48 J + S 85

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Inequality Symbols < means less than > means greater than less than or equal to means greater than or equal to means not equal

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Solving Inequalities and their Graphs

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