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Write and Graph Inequalities Honors Math – Grade 8

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Get Ready for the Lesson The Rockville School wants to donate at least $1500 to a relief fund. The student council decides to raise the money through a student car wash. The cost for customers will be $12 per car. What algebraic sentence can be written to represent the number of cars that will be needed in order to raise at leat the intended amount? Write an inequality to represent this situation. An inequality is a statement that compares to expressions or quantities that may not be equal. It uses one or more comparison symbols. To write an inequality: Look for key words associated with inequality symbols. Associate the remaining word phrases with symbols and use a variable for the unknown quantity. Algebraic Word SentenceComparison Symbol a is less than b a is greater than b a is less than or equal to b a is at most b a is greater than or equal to b a is at least b a is not equal to b

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Compound Inequality containing and Two inequalities connected by the word and form a compound inequality. A compound inequality containing “and” is true only if both inequalities are true. Its graph is the intersection of the graphs of the two inequalities. The solution must satisfy both inequalities. A compound inequality joined by the word AND is called a conjunction.

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Graph the solution set of the compound inequality. x -2 Graph the 1 st inequality. x < 3 Graph the 2 nd inequality. x > -2 Find the intersection. Where do the graphs overlap? This represents the intersection. The solution set is: -2 < x < 3

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Graph the solution set of the compound inequality. p 2 Graph the 1 st inequality. p < 6 Graph the 2 nd inequality. p > 2 Find the intersection. Where do the graphs overlap? This represents the intersection. The solution set is: 2 < p < 6

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Graph the solution set of the compound inequality. -5 < x – 4 < 2 1. Express -5 < x – 4 < 2 using and. Then solve each inequality. -1 < x Graph the 2 nd inequality. x < 6 Find the intersection. Where do the graphs overlap? This represents the intersection. The solution set is: -1 < x < 6 -5 < x – 4 and x – 4 < 2 -1 < x and x < 6 Graph the 1 st inequality.

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Graph the solution set of the compound inequality. 6 < r + 7 < 10 1. Express 6 < r + 7 < 10 using and. Then solve each inequality. -1 < r Graph the 2 nd inequality. r < 3 Find the intersection. Where do the graphs overlap? This represents the intersection. The solution set is: -1 < r < 3 6 < r + 7 and r + 7 < 10 -1< r and r < 3 Graph the 1 st inequality.

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