Question 1

Solve the equation $$x - \frac{7}{8} = 3x + \frac{1}{10}. $$What is the value of $$x$$?

Accepted Answer

$$x = \frac{39}{80}$$

Question 2

Solve the equation $$-x = 1 - \frac{5(x-5)}{6}. $$What is the value of $$x$$?

Accepted Answer

$$x = -93$$

Question 3

Solve the equation $$x + \frac{4}{5} = \frac{1}{7}x + \frac{1}{3}. $$What is the value of $$x$$?

Accepted Answer

$$x = \frac{49}{75}$$

Question 4

Solve the equation $$4[3(x-13)-2(2x+2)] = 5[x-6-3(3x-4)]. $$What is the value of $$x$$?

Accepted Answer

$$x = \frac{131}{23}$$

Question 5

Given the function $$f(x) = \frac{8}{3}x - 8$$, what is the zero of $$f(x)$$?

Accepted Answer

$$x = 3$$

Question 6

A table shows $$f(6) = 0$$ and $$f(0) = -38. $$What is the $$x-$$intercept of the graph of $$y = f(x)$$?

Accepted Answer

$$x = 6$$

Question 7

Given the function $$f(x) = 190 + 20x$$, what is the solution to $$f(x) = 0$$?

Accepted Answer

$$x = -9.5$$

Question 8

Solve the equation $$16x - 49 = 20 - 7x$$ using a graphical method. What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 9

Solve the equation $$-4 = \frac{3t}{4} + \frac{8t-1}{3}$$ using a graphical method. What is the value of $$t$$?

Accepted Answer

$$t = -4$$

Question 10

Solve the formula $$G = P(1 + rt)$$ for $$t. $$What is the solution?

Accepted Answer

$$t = \frac{G - P}{Pr}$$

Question 11

Solve for $$x in $$the equation $$B + H = Mx. $$What is the solution?

Accepted Answer

Question 12

Solve for $$y in $$the equation $$9x - 4y = 9. $$What is the solution?

Accepted Answer

Question 13

The profit from the production and sale of specialty golf hats is given by $$P(x) = 20x - 2000. $$How many hats must be produced and sold to avoid a loss?

Accepted Answer

$$x = 100$$

Question 14

A company wants to make a profit of $$8000$$ from selling golf hats, where $$P(x) = 20x - 2000. $$How many hats must be produced and sold?

Accepted Answer

$$x = 500$$

Question 15

Given the function $$f(x) = \frac{8}{3}x - 8$$, what is the $$x-$$intercept of the graph?

Accepted Answer

$$x = 3$$

Question 16

If a function $$f(x)$$ has a zero at $$x = 40$$, what is the $$x-$$intercept of the graph of $$y = f(x)$$?

Accepted Answer

$$x = 40$$

Question 17

Which of the following is the correct strategy to solve an equation with fractions, such as $$x + \frac{4}{5} = \frac{1}{7}x + \frac{1}{3}$$?

Accepted Answer

Multiply each term by the least common denominator (LCD) of all fractions.

Question 18

In a real-world scenario, a medical researcher models the growth of bacteria with $$N(t) = N_0$ e$$^{rt}$$. If N_0$ = 100$$ and $$r = 0.05$$, how long will it take for the population to double?

Accepted Answer

$$t = \frac{\ln 2}{0.05}$$

Question 19

A chemical reaction is modeled by $$C(t) = 50 - 4t. $$After how many hours will the concentration reach zero?

Accepted Answer

$$t = 12.5$$

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