Question 1

Solve for $$x$$: $$x^2$$ = $$3x^4 + 5$.

Accepted Answer

Question 2

Solve for $$x$$: $$\dfrac{5}{2x} - \dfrac{8}{9} = \dfrac{1}{18} - \dfrac{1}{3x}.$$

Accepted Answer

$$x = 6$$

Question 3

Simplify $$\sqrt{32}$$ and write your answer in simplest radical form.

Accepted Answer

$$4\sqrt{2}$$

Question 4

Factor completely: $$x^3$$ + $$2x^2 - 9x - 18$.

Accepted Answer

$$(x + 2)(x - 3)(x + 3)$$

Question 5

Solve by factoring: $$x^2 - 15x + 36 = 0$.

Accepted Answer

$$x = 12, x = 3$$

Question 6

Solve by the square root method and write the solution in exact form: $$(x - 7)^2$ = 20.$$

Accepted Answer

$$x = 7 \pm 2\sqrt{5}$$

Question 7

Solve by completing the square and write the solution in exact form: $$x^2 + 6x - 3 = 0$.

Accepted Answer

$$x = -3 \pm 2\sqrt{6}$$

Question 8

A machine produces open boxes by cutting $$5-$$inch squares from each corner of a square sheet and folding up the sides. If the volume of the box must be $$2000$$ cubic inches, what is the length of a side of the original square sheet? (Let $$x be $$the length of the side of the original square sheet.)

Accepted Answer

$$x = 25$$

Question 9

Solve for $$x$$: $$5x^4$$ - $$45x^2 = 0$.

Accepted Answer

$$x = 0, x = \pm 3$$

Question 10

Solve for $$x$$: $$1 - 2x = x + 7.$$

Accepted Answer

$$x = -2$$

Question 11

Solve for $$x$$: $$(x + 5$$)^{2/3}$$ = 4.$$

Accepted Answer

$$x = 11$$

Question 12

Solve: $$|5x + 2| + 4 = 13.$$

Accepted Answer

$$x = \dfrac{11}{5} or$$ $$x = -3$$

Question 13

Solve and express the solution using interval notation: $$\dfrac{x}{6} - \dfrac{1}{6} \leq \dfrac{x}{3} + 2.$$

Accepted Answer

$$(-\infty, 25]$$

Question 14

Solve and express the solution using interval notation: $$\dfrac{x - 2}{3} \geq \dfrac{x - 4}{4} + \dfrac{7}{12}.$$

Accepted Answer

$$[6, \infty)$$

Question 15

Solve and express the solution using interval notation: $$|x + 1| + 3 \leq 9.$$

Accepted Answer

$$[-7, 5]$$

Question 16

Solve and express the solution using interval notation: $$-2|x - 4| \u003c -4.$$

Accepted Answer

$$(-\infty, 2) \cup (6, \infty)$$

Question 17

Rewrite $$64^{-2/3} as a $$radical in simplest form.

Accepted Answer

$$\dfrac{1}{16}$$

Question 18

Factor completely: $$48y^4$$ - $$3y^2.$$

Accepted Answer

$$3y^2(16y^2$ - 1)$

Question 19

Solve using the quadratic formula and write the solution in exact form: $$2x^2 = 4x - 3$.

Accepted Answer

$$x = 1 \pm \dfrac{\sqrt{10}}{2}$$

College Algebra Practice Set I – Step-by-Step Guidance

Study Guide - Practice Questions

Study Guide - Flashcards