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Math Journal 10-16

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Math Journal 10-15

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Unit 3 Day 7: Solving Inequalities with Variables on Both Sides Essential Questions: How do we solve inequalities with variables on both sides? When does an inequality have no solution or a solution of all real numbers?

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Vocabulary No solution: when the variable in an equation or inequality is eliminated and you are left with a false statement All real numbers: when the variable in an equation or inequality is eliminated and you are left with a true statement

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Example 1: Solve the inequalities. 7x + 19 > -2x + 556x + 22 < -3x + 31 + 2x 9x+ 19> 55 - 19 9x> 36 9 9 x> 4 + 3x 9x+ 22< 31 - 22 9x < 9 9 9 x< 1

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Example 2: Solve the inequalities. x + 2 > 3x + 1-8x + 7 < 4x 5 - 3x -2x + 2> 1 - 2 -2x> -1 -2 - 4x -12x + 7< - 5 - 7 -12x< -12 -12 x < 2 1 x > 1 -12

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Example 3: Solve the inequality. (-12x + 16) < 10 3(-x 2) + 4-3x < 10 -3x+ 4 < 16 - 3x -6x + 4< 16 + 3x - 4 -6x< 12 + 6 + 3x -6 x > -2 4 1 -6

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Example 4: Solve the inequality. (12x 4) < 2(7 5x) - 26x< 14 + 10x 16x- 2< 14 - 10x + 2 + 10x 16 x < 1 16x< 16 2 1 16

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Example 5: Solve the inequalities. 12 2a 3 x + 5a 12+ 3a< - 9 - 12 3a< - 21 3 3 a < -7 - x + 3> 3 - x + x 3 > 3 true statement infinite solutions

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- 5x < 5x- 25 - 5x + 24 5x 24 < -25 false statement no solutions 6y- 3y 3y + 6 > 5y - 4 - 5y > 5y + 6 - 4 - 6 - 4-2y + 6> -2 Example 6: Solve the inequalities. 5x + 24 5y - 4 > -10 -2y y < 5 -2

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Example 7: Phone Company A charges an activation fee of 36 cents and then 3 cents per minute. Phone Company B charges 6 cents per minute with no activation fee. For what value of x is Phone Company A more expensive than Phone Company B?.36 +.03x >.06x -.03x.36 >.03x 12 > x Phone Company A is more expensive when the number of minutes is less than 12. If you talk for more than 12 minutes, Phone Company A is a good choice..03 x < 12

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Example 8: Justin and Tyson are beginning an exercise program to train for football season. Justin weighs 150 pounds and hopes to gain 2 pounds per week. Tyson weighs 195 pounds and hopes to lose 1 pound per week. If the plan works, for how many weeks will Justin weigh less than Tyson? JustinTyson 150 + 2x + 1x 150 + 3x < 195 - 150 3x < 45 x < 15 Justin will weigh less than Tyson up until the 15 week mark. < 195 - 1x 33

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Summary Essential Questions: How do we solve inequalities with variables on both sides? When does an inequality have no solution or a solution of all real numbers? Take 1 minute to write 2 sentences answering the essential question.