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MFCR Unit 2 Performance Task 1. Is 9 a solution of 2x - 12 = 18? Justify your answer mathematically and in words. 2. One group turned in the following solution to an equation but noted that the answer they found did not check. Find the errors in their work and explain what they did wrong. Give the correct solution. 33 = 3(6 + π₯) 33 = 3(π₯ + 6) 33 = 3π₯ + 6 33 β 6 = 3π₯ + 6 β 6 27 = 3π₯ + 0 27 = 3π₯ 3π₯ = 27 1 1 β 3π₯ = 3 β 27 3 1γ»π₯ = 9 π₯=9 Check: 33 = 3(6 + π₯) 33 ? 3(6 + 9) 33 ? 3(15) 33 β 45 Since π₯ Original equation Commutative Property Distributive Property Subtraction Property of Equality Additive Inverse Identity Element of Addition Symmetric Property Multiplication Property of Equality Multiplicative Inverse Identity Element of Multiplication = 9 does not check, it is not a solution. 3. Another group felt that their work was correct but was not sure they had provided the correct reason for each step. Look over the work below and explain to the group which reasons to change. 9 β π₯ = (3π₯ + 3) β 14 9 β π₯ = 3π₯ + (3 β 14) 9 β π₯ = 3π₯ β 11 9 β π₯ + 11 = 3π₯ β 11 + 11 9 + 11 β π₯ = 3π₯ + 0 20 β π₯ = 3π₯ 20 β π₯ + π₯ = 3π₯ + π₯ 20 + 0 = 4π₯ 20 = 4π₯ 4π₯ = 20 1 1 β 4π₯ = 4 β 20 4 1γ»π₯ = 5 π₯=5 Original equation Distributive Property Simplify Addition Property of Equality Commutative Property Simplify, Identity Element of Addition Addition Property of Equality Identity Element of Addition Additive Inverse Symmetric Property Multiplicative Inverse Multiplication Property of Equality Identity Element of Multiplication 4. Consider the equation 3π₯ + 6 = 2(8 β π₯). β’ Solve this equation for x. β’ Provide an explanation or justification for your work. β’ Check by substituting your answer back into the original equation and showing that it simplifies to a true statement. For safe swimming, pool water chemistry needs to be maintained at proper levels. For example, βfree available chlorineβ should never fall below 2.0 ppm (parts per million) and the βcombined available chlorineβ levels should be less than 0.2 ppm. 5. Write and graph an inequality for the recommended levels of free available chlorine, f. 6. Write and graph an inequality for the recommended levels of combined available chlorine, c. 7. Joe tested his pool water and got these results: f = 2.0 ppm and c = 0.4 ppm. Explain whether or not the pool water falls within the proper levels. In addition to chlorine, other chemicals also help maintain proper levels. Joeβs pool water test kit includes the following label. Use the table to answer the questions below. Safe Pool Chemical Levels Chemical Recommended Level Free available chlorine, ppm 2.0 β 4.0 Combined available chlorine, ppm < 0.2 pH level 7.5 (plus/minus 0.3) Total alkalinity, ppm 80 β 100 Total dissolved solids, ppm not to exceed 1500 greater than at pool start-up Calcium hardness, ppm 200 β 400 Cyanuric acid, ppm 30 β 50 8. Write and graph on a number line the compound inequality that represents the recommended levels of free available chlorine, f. 9. When Joe filled the pool for the summer, the total dissolved solids measured 500 ppm. a. Write an inequality to figure out if the total dissolved solids s in his pool are at the recommended level. b. Give an example of a safe level of dissolved solids s. 10. The inequality |x β 7.5| β€ 0.3 determines proper pH levels. Solve this inequality and interpret the solution.