Question 1

Solve the rational equation: $$\frac{4}{x(x-1)} = \frac{2}{x} + \frac{7}{x-1}.$$

Accepted Answer

$$x = 2$$

Question 2

Which of the following is the solution to the absolute value equation $$2|x-5| = 14$$?

Accepted Answer

$$x = 12 or$$ $$x = -2$$

Question 3

A company’s profit $$P (in $$thousands of dollars) is modeled by the equation $$P = 2x^2$ - 4x - 6$$, where $$x is $$the number of units sold (in thousands). What is the minimum profit, and for how many units sold does it occur?

Accepted Answer

Minimum profit is $$-10 at$$ $$x = 1$$

Question 4

Solve the linear equation: $$4(x+2) = 3x - 6.$$

Accepted Answer

$$x = -14/3$$

Question 5

Which of the following is the solution to the quadratic equation $$2x^2 + 12x + 10 = 0$?

Accepted Answer

$$x = -3 \pm \sqrt{2}$$

Question 6

A stock investment problem: If you invest $$\50$$,000$$ in two stocks, one yielding 5$$\%$$ and the other 8$$\%$$, and you want a total annual return of $$\$$3,400$$, how much should you invest in each stock?

Accepted Answer

$$\30$$,000$$ at 5$$\%$$, $$\$$20,000 at$$ $$8\%$$

Question 7

Solve the inequality: $$2x - 5 \u003c 7.$$

Accepted Answer

$$x \u003c 6$$

Question 8

Which of the following is the solution to the radical equation $$\sqrt{2x + 10} = 2x - 2$$?

Accepted Answer

$$x = 3$$

Question 9

Solve for $$x in $$the quadratic equation $$x^2 - 4x + 5 = 0$.

Accepted Answer

$$x = 2 \pm i$$

Question 10

If $$|2x - 1| \u003e 5$$, which of the following intervals describes the solution set?

Accepted Answer

$$x  3$$

Question 11

Which of the following is the correct solution to the equation $$x^2 + 8x + 17 = 0$?

Accepted Answer

$$x = -4 \pm i$$

Question 12

A chemist needs to mix a $$10\%$$ saline solution with a $$30\%$$ saline solution to obtain $$100 mL of a$$ $$20\%$$ solution. How many mL of each solution should be used?

Accepted Answer

$$50 mL of$$ $$10\%$$, $$50 mL of$$ $$30\%$$

Question 13

Solve the equation $$|x+4| = 2x - 6$$ for real solutions.

Accepted Answer

$$x = 5$$

Question 14

Which of the following is the solution to the inequality $$x^2 - 4x + 3$$ \u003c 0$$?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 15

If $$x is a $$real number such that $$x^2 + 2x + 2 = 0$, what is the value of x$?

Accepted Answer

$$x = -1 \pm i$$

Algebra Practice Problems: Key Precalculus Topics

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