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Situations That Always or Never Happen

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Job A = 30,000 + 5000yJob B = 28,000 + 5000y When is the pay in Job A better than the pay in Job B? Write an equation or inequality to represent the situation. Solve.

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Since 30,000 > 28,000 is always true, the disappearance of y signals that y can be any real number. Job A will always pay better than Job B.

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Job A = 30,000 + 5000yJob B = 28,000 + 5000y When is the pay in Job A less than the pay in Job B? Write an equation or inequality to represent the situation. Solve.

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Since 30,000 < 28,000 is never true, the disappearance of y signals that y can be any real number. Job A will never pay less than Job B.

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If you are solving and the variable disappears…

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Follow the steps to solve ax + b = cx + d or ax + b < cx + d. Look at end result to determine if the resulting sentence is true (will always happen all real solutions) or false (will never happen no real solution) Check by looking at a graph.

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Using your graphing calculator, set Y 1 = left side of equation or inequality and Y 2 = right side of equation or inequality for equations (ax + b = cx + d) If lines are parallel (never cross) no real solution If lines overlap (looks like one line) all real solutions If lines cross x value of intersection point is solution for inequalities (ax + b < cx + d) If lines are parallel, line to the left > line to right, line to right < line to left Use above information to compare to original statement to determine if true or false. If lines overlap (looks like one line) no real solutions (if ), all real numbers (if ≤ or ≥) If lines cross x value of intersection point is solution

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Solve 18m – 20 + 3m = 3(7m + 2) Follow the steps to solving ax + b = cx + d Look at the result and determine if it is a true or false statement. Check with a graph.

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Solve 42k < 80k + 6 – 38k Follow the steps to solving ax + b < cx + d Look at the result and determine if it is a true or false statement. Check with a graph.

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Solve 7x – 10 – 3x = 2(2x – 4)

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1. Hamburger Heaven pays a starting salary of $6.90 an hour, and each year increases it by $1 an hour. Video King starts at $7.50 an hour and also increases $1 an hour per year. a. Write an expression representing the salary of Hamburger Heaven and one representing the salary of Video King. b. Use algebra to determine when does Hamburger Heaven pay more? 2. Solve 40 – 2x = 11 + 29 – 2x

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1. Hamburger Heaven pays a starting salary of $6.90 an hour, and each year increases it by $1 an hour. Video King starts at $7.50 an hour and also increases $1 an hour per year. a. H = 6.90 + yV = 7.50 + y b. 6.90 + y > 7.50 + y 6.90 > 7.50 no solution so, Hamburger Heaven never pays more. 2. 40 = 40 true all real solutions

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