Question 1

Given the equation $$x = yz$$, solve for $$y.$$

Accepted Answer

$$y = \frac{x}{z}$$

Question 2

If $$x = yz$$ and $$x = 24$$ and $$z = 6$$, what is the value of $$y$$?

Accepted Answer

$$y = 4$$

Question 3

Which property of equality is used when dividing both sides of $$x = yz by$$ $$z to $$solve for $$y$$?

Accepted Answer

Multiplication property of equality

Question 4

A chemist uses the formula $$x = yz to $$calculate the concentration of a solution. If the total amount $$x is $$halved and $$z$$ remains constant, what happens to $$y$$?

Accepted Answer

$$y is $$halved

Question 5

If $$x = yz$$ and $$y = 0$$, what must be true about $$x$$?

Accepted Answer

$$x = 0$$

Question 6

Solve for $$z in $$the equation $$x = yz.$$

Accepted Answer

$$z = \frac{x}{y}$$

Question 7

A medical researcher uses $$x = yz to $$relate dosage ($$x$$), concentration ($$y$$), and volume ($$z). If $$the dosage is $$50 mg $$and the volume is $$10 mL$$, what is the concentration?

Accepted Answer

$$5 mg/mL$$

Question 8

Which of the following steps is NOT valid when solving $$x = yz$$ for $$y$$?

Accepted Answer

Subtract $$z$$ from both sides

Question 9

If $$x = yz$$ and $$z = 0$$, what can you conclude about $$x$$?

Accepted Answer

$$x = 0$$

Question 10

A recipe uses the formula $$x = yz to $$determine the total amount of an ingredient needed. If $$y = 3$$ and $$z = 8$$, what is $$x$$?

Accepted Answer

$$x = 24$$

Question 11

If $$x = yz$$ and you want to solve for $$y$$ but $$z = 0$$, what should you be careful about?

Accepted Answer

Division by zero is undefined

Question 12

Which of the following real-world scenarios can be modeled by the equation $$x = yz$$?

Accepted Answer

Calculating the area of a rectangle with length $$y$$ and width $$z$$

Question 13

If $$x = yz$$ and $$x = 0$$, which of the following must be true?

Accepted Answer

Either $$y = 0 or$$ $$z = 0$$

Question 14

A physics formula uses $$x = yz to $$relate force ($$x$$), mass ($$y$$), and acceleration ($$z). If $$the force is $$20 N $$and the mass is $$4 kg$$, what is the acceleration?

Accepted Answer

$$5$$ $$m/s^2$

Question 15

If $$x = yz$$ and you double $$z$$ while keeping $$x$$ constant, what happens to $$y$$?

Accepted Answer

$$y is $$halved

Solving Formulas for a Specified Variable: Isolating Variables in Equations

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