Question 1

Which of the following operations will NOT always result in an equivalent equation?

Accepted Answer

Multiplying both sides by zero.

Question 2

Given the equation $$2x - 3y = 6$$, which of the following is the correct expression for $$y in $$terms of $$x$$?

Accepted Answer

$$y = \frac{2}{3}x - 2$$

Question 3

If you multiply both sides of the equation $$x - 4 = 7 by$$ $$-1$$, what is the resulting equation?

Accepted Answer

$$-x + 4 = -7$$

Question 4

Which of the following is a valid step in transforming $$3y + 2 = 8 to $$solve for $$y$$?

Accepted Answer

Subtract 2 from both sides to get $$3y = 6$$

Question 5

A student rewrites the equation $$4x - 5y = 10 as$$ $$y = \frac{4}{5}x - 2. $$Which property did the student use?

Accepted Answer

Isolating $$y by $$subtracting $$4x$$ from both sides and then dividing by $$-5$$

Question 6

Which of the following equations is NOT equivalent to $$2x + 3 = 7$$?

Accepted Answer

$$x = 4$$

Question 7

Suppose you have the equation $$5y - 2x = 15. $$What is $$y in $$terms of $$x$$?

Accepted Answer

$$y = \frac{2}{5}x + 3$$

Question 8

Which of the following is a necessary step to graph the equation $$y = 2x - 5$$ using a graphing utility?

Accepted Answer

Input the equation as $$y = 2x - 5$$ into the utility.

Question 9

A chemical reaction is modeled by the equation $$3A + 2B = 12. If$$ $$A is $$increased by 1, how must $$B$$ change to keep the equation balanced?

Accepted Answer

$$B$$ must decrease by $$1.5$$

Question 10

Which of the following is an example of using the distributive property to create an equivalent equation?

Accepted Answer

Changing $$2(x + 3) = 10 to$$ $$2x + 6 = 10$$

Question 11

If you subtract $$x$$ from both sides of the equation $$x + y = 5$$, what is the resulting equation?

Accepted Answer

$$y = 5 - x$$

Question 12

A business's profit is modeled by $$P = 3x - 7. If $$the profit is zero, what is the value of $$x$$?

Accepted Answer

$$x = \frac{7}{3}$$

Graph Equations and Equivalent Equations in Precalculus

Study Guide - Practice Questions