Question 1

Solve for $$k in $$the equation $$\displaystyle \frac{6 - 3k}{7} = 3.$$

Accepted Answer

$$k = -5$$

Question 2

Which of the following is the solution set for the inequality $$-10 - 10v - 9 \u003c 21$$?

Accepted Answer

$$-4 \u003c v \u003c 2$$

Question 3

Solve the quadratic equation by completing the square: $$k^2 + 2k - 39 = 9$.

Accepted Answer

$$k = 6 or$$ $$k = -8$$

Question 4

A floor is 14 feet longer than its width. The area of the floor is 1632 square feet. Which quadratic equation represents the area in terms of width $$w$$?

Accepted Answer

$$w(w + 14) = 1632$$

Question 5

Solve for $$x in $$the equation $$-2(3x + 8) - 4 = x + 22.$$

Accepted Answer

$$x = -6$$

Question 6

Which of the following is the solution to $$x^2 - 35 = -2x$?

Accepted Answer

$$x = 5 or$$ $$x = -7$$

Question 7

Solve for $$n in $$the equation $$3 - 4n^2$ = -1.$$

Accepted Answer

$$n = 1 or$$ $$n = -1$$

Question 8

Solve the rational equation $$\displaystyle \frac{1}{3b} = \frac{1}{6b} + 1$$ for $$b.$$

Accepted Answer

$$b = \frac{1}{6}$$

Question 9

Which of the following is the solution set for the compound inequality $$-42 \u003c 5n - 2 \u003c 13$$?

Accepted Answer

$$-8 \u003c n \u003c 3$$

Question 10

Solve for $$x in $$the equation $$\displaystyle (x - 1$$)^{2/3}$$ - 25 = 0.$$

Accepted Answer

$$x = 126 or$$ $$x = -124$$

Question 11

A rational equation is given by $$\displaystyle \frac{6 - 6n}{n + 6} = 1. $$What is the solution for $$n$$?

Accepted Answer

$$n = 0$$

Question 12

Solve for $$m$$ using the quadratic formula: $$7m^2 - 5m = 4$ (rounded to three decimal places).

Accepted Answer

$$m = 1.193 or$$ $$m = -0.479$$

Question 13

Which of the following is the correct solution for $$v in$$ $$9v^2 - 8 = -31$?

Accepted Answer

$$v = \pm \displaystyle \frac{\sqrt{23} \cdot i}{3}$$

Question 14

Solve for $$x in $$the equation $$u = xk + y$$ for $$x.$$

Accepted Answer

$$x = \displaystyle \frac{u - y}{k}$$

Question 15

A compound inequality is given by $$49 \u003c 7 - 7r \leq 63. $$What is the solution set for $$r$$?

Accepted Answer

$$-8 \leq r \u003c -6$$

Question 16

Solve for $$x in $$the equation $$\displaystyle (12 - x$$)^{1/3}$$ - 3 = 0.$$

Accepted Answer

$$x = -15$$

Question 17

A floor is 14 feet longer than its width. The area is 1632 square feet. What are the dimensions of the floor?

Accepted Answer

Width = 32 ft, Length = 46 ft

Question 18

Solve for $$k in $$the equation $$4k^2 - 10 = -18k$ by factoring.

Accepted Answer

$$k = \frac{1}{2} or$$ $$k = -5$$

Precalculus Study Guide: Equations, Inequalities, Quadratics, and Rational Functions

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