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Section 3-3 Solve Inequalities using Multiplication & Division SPI 22N: identify the graphical representation of the solution to a one variable inequality Objectives: Use multiplication and division to solve inequalities Consider the inequality 4 > 1. 1. Complete each statement at the right with the appropriate inequality sign. 4 ∙ 3 1 ∙ 3 4 ∙ 2 1 ∙ 2 4 ∙ 1 1 ∙ 1 4 ∙ 0 1 ∙ 0 4 ∙ -1 1 ∙ -1 4 ∙ -2 1 ∙ -2 4 ∙ -3 1 ∙ -3 > > > = < < < 2. What happens to the symbol when you multiply each side by a positive number? 3. What happens to the symbol when you multiply each side by 0? 4. What happens to the symbol when you multiply each side by a negative number?

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Multiplication Property of Inequality: For every real number a and b, and for c < 0 Properties of Inequalities if a > b then ac < bc... and... if a bc If a = 4, b = 2 and c = -2... Then... 4 > 2 and 4(-2) < 2(-2) If c > 0, solve like an equality.

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Division Property of Inequality: For every real number a and b, and for c < 0 Properties of Inequalities if a > b then a < b... and... c c if a b c c If a = 4, b = 2 and c = -2... Then... 4 > 2 and 4 < 2 -2 -2 If c > 0, solve like an equality.

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Solve the inequality Solve using the Properties of Inequalities Since you have to divide by a negative number, change the inequality sign Simplify

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Solve the inequality Solve using the Properties of Inequalities Multiply each side by the reciprocal of the coefficient of y. Do not change the sign, because you are not multiplying by a negative value. Simplify

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Your family budgets $160 to spend on fuel for a trip. How many times can they fill the car’s gas tank if it cost $25 each time? Solve using the Properties of Inequalities Define a variable for the unknown: x = number of times car can be filled 25x ≤ 160 Write an Inequality: 25x ≤ 160 25 Solve the Inequality x ≤ 6.4 Answer the question: The car can be filled at least 6 times.

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