Question 1

Given the equation $$Z = AB - 4$$, which of the following correctly solves for $$A in $$terms of $$Z$$ and $$B$$?

Accepted Answer

$$A = \frac{Z + 4}{B}$$

Question 2

If $$Z = AB - 4$$ represents the relationship between the number of bacteria ($$Z$$), antibiotic concentration ($$A$$), and time ($$B$$), what happens to $$A if$$ $$Z$$ increases by 10 units, assuming $$B$$ remains constant?

Accepted Answer

$$A$$ increases by $$\frac{10}{B}$$

Question 3

Which property of equality is used first to isolate $$A in $$the equation $$Z = AB - 4$$?

Accepted Answer

Addition property of equality

Question 4

After isolating $$A in$$ $$Z = AB - 4$$, what is the next step to solve for $$A$$?

Accepted Answer

Divide both sides by $$B$$

Question 5

A medical researcher uses the formula $$Z = AB - 4 to $$calculate dosage. If $$Z = 16$$ and $$B = 2$$, what is the value of $$A$$?

Accepted Answer

$$A = \frac{16 + 4}{2} = 10$$

Question 6

If $$A = \frac{Z + 4}{B}$$, what is the value of $$Z$$ when $$A = 5$$ and $$B = 3$$?

Accepted Answer

$$Z = 11$$

Question 7

Which of the following best describes the process of solving $$Z = AB - 4$$ for $$A$$?

Accepted Answer

Add 4 to both sides, then divide by $$B$$

Question 8

A chemist needs to solve for $$A in$$ $$Z = AB - 4. If$$ $$Z = 20$$ and $$B = 4$$, what is $$A$$?

Accepted Answer

$$A = \frac{20 + 4}{4} = 6$$

Question 9

If $$Z = AB - 4$$ and $$A is $$doubled while $$B$$ remains constant, what happens to $$Z$$?

Accepted Answer

$$Z$$ increases by $$AB$$

Question 10

Which of the following is NOT a valid step in solving $$Z = AB - 4$$ for $$A$$?

Accepted Answer

Multiply both sides by $$B$$

Question 11

A student incorrectly solves $$Z = AB - 4$$ for $$A$$ and gets $$A = \frac{Z - 4}{B}. $$What mistake did the student make?

Accepted Answer

Subtracted 4 instead of adding 4 to both sides

Question 12

If $$Z = AB - 4$$ and $$B = 0$$, what is the value of $$A$$?

Accepted Answer

$$A is $$undefined

Question 13

In a real-world scenario, $$Z = AB - 4$$ models the cost ($$Z) of $$producing $$A$$ units at $$B$$ dollars per unit, minus a fixed discount of $$4. If $$the cost is $$36$$ and the price per unit is $$8$$, how many units were produced?

Accepted Answer

$$A = \frac{36 + 4}{8} = 5$$

Question 14

If $$A = \frac{Z + 4}{B}$$, which of the following statements is true?

Accepted Answer

As $$B$$ increases, $$A$$ decreases if $$Z is $$constant

Question 15

Which equation represents the inverse operation of solving $$Z = AB - 4$$ for $$A$$?

Accepted Answer

$$A = \frac{Z + 4}{B}$$

Solving Linear Equations for a Specified Variable

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