Question 1

Solve the rational equation for $$x$$: $$\frac{2}{x} + 1 = \frac{5}{x}.$$

Accepted Answer

$$x = 2$$

Question 2

Solve for $$x$$: $$\sqrt{x + 5} = 4.$$

Accepted Answer

$$x = 9$$

Question 3

Solve for $$x$$: $$x^{3/2} = 8$.

Accepted Answer

$$x = 4$$

Question 4

Solve the inequality: $$3x - 7 \u003c 2x + 5.$$

Accepted Answer

$$x \u003c 12$$

Question 5

Solve the quadratic inequality: $$x^2 - 4$$ \u003c 0$$.

Accepted Answer

$$-2 \u003c x \u003c 2$$

Question 6

Solve the rational inequality: $$\frac{x-1}{x+2} \u003e 0.$$

Accepted Answer

$$x \u003e 1 or$$ $$x \u003c -2$$

Question 7

Solve the absolute value equation: $$|2x - 3| = 7.$$

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 8

Solve the absolute value inequality: $$|x + 4| \leq 6.$$

Accepted Answer

$$-10 \leq x \leq 2$$

Question 9

Given points $$A(2, 3)$$ and $$B(6, 11)$$, what is the distance between them?

Accepted Answer

$$2\sqrt{17}$$

Question 10

Given points $$A(-1, 4)$$ and $$B(5, -2)$$, what is the midpoint of the segment joining them?

Accepted Answer

$$(2, 1)$$

Question 11

Which of the following is an ordered pair solution to the equation $$y = 2x + 1$$?

Accepted Answer

$$(1, 3)$$

Question 12

Identify the center and radius of the circle given by $$x^2$$ + $$y^2 - 4x + 6y = 12$.

Accepted Answer

Center $$(2, -3)$$, radius $$5$$

Question 13

What is the equation of a circle with center $$(1, -2)$$ and radius $$4$$?

Accepted Answer

$$(x - 1)^2$ + (y + 2)^2$ = 16$$

Question 14

Evaluate the function $$f(x) = 3x^2$ - 2x + 1 at$$ $$x = -1.$$

Accepted Answer

$$6$$

Question 15

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1,2), (2,3), (1,4)\}$$

Question 16

Which of the following is the graph of the line $$y = -2x + 3$$?

Accepted Answer

A line with slope $$-2$$ and $$y-$$intercept $$3$$

Question 17

A chemist mixes a solution with concentration $$c(x) = \frac{2x}{x+1}$$, where $$x is $$the amount of solute in grams. What is the concentration when $$x = 3$$?

Accepted Answer

$$\frac{6}{4} = 1.5$$

Question 18

Solve for $$x$$: $$\sqrt{2x + 1} = x + 1.$$

Accepted Answer

$$x = 1$$

Question 19

Solve the equation with rational exponents: $$x^{2/3} = 9$.

Accepted Answer

$$x = 27$$

Question 20

A company’s profit $$P is $$modeled by $$P(x) = -x^2$ + 6x - 5$$, where $$x is $$the number of units sold. For what values of $$x is $$the profit positive?

Accepted Answer

$$1 \u003c x \u003c 5$$

Essential College Algebra Study Guide: Equations, Inequalities, Functions, and Analytic Geometry

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