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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 βˆ’ 6 = 3π‘₯ + 6 βˆ’ 6
27 = 3π‘₯ + 0
27 = 3π‘₯
3π‘₯ = 27
1
1
βˆ™ 3π‘₯ = 3 βˆ™ 27
3
1・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 βˆ’ π‘₯ = (3π‘₯ + 3) βˆ’ 14
9 βˆ’ π‘₯ = 3π‘₯ + (3 βˆ’ 14)
9 βˆ’ π‘₯ = 3π‘₯ βˆ’ 11
9 βˆ’ π‘₯ + 11 = 3π‘₯ βˆ’ 11 + 11
9 + 11 βˆ’ π‘₯ = 3π‘₯ + 0
20 βˆ’ π‘₯ = 3π‘₯
20 βˆ’ π‘₯ + π‘₯ = 3π‘₯ + π‘₯
20 + 0 = 4π‘₯
20 = 4π‘₯
4π‘₯ = 20
1
1
βˆ™ 4π‘₯ = 4 βˆ™ 20
4
1・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 βˆ’ 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, β€œfree
available chlorine” should never fall below 2.0 ppm (parts per million) and the β€œcombined available
chlorine” 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. Joe’s 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 – 4.0
Combined available chlorine, ppm
< 0.2
pH level
7.5 (plus/minus 0.3)
Total alkalinity, ppm
80 – 100
Total dissolved solids, ppm
not to exceed 1500 greater than at pool start-up
Calcium hardness, ppm
200 – 400
Cyanuric acid, ppm
30 – 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 βˆ’ 7.5| ≀ 0.3 determines proper pH levels. Solve this inequality and interpret the
solution.