Question 1

Simplify the expression $$4(2x - 3) - 5(x + 1). $$What is the result?

Accepted Answer

$$3x - 17$$

Question 2

Which of the following is the correct scientific notation for $$0.00032$$?

Accepted Answer

$$3.2 	imes 10$$^{-4}$$

Question 3

Factor the expression $$6x^2 + 5x - 6$.

Accepted Answer

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

Question 4

Simplify the rational expression $$\frac{x^2$ - 9}{x - 3}$$, assuming $$x 
eq 3.$$

Accepted Answer

$$x + 3$$

Question 5

Find the slope of the line passing through the points $$(0, 0)$$ and $$(3, 2).$$

Accepted Answer

$$\frac{2}{3}$$

Question 6

A car rental company charges a flat fee of $$40 plus 0.25 $$per mile. Another company charges $$30 plus 0.35 $$per mile. For how many miles will the cost be the same?

Accepted Answer

$$100$$

Question 7

Solve the equation $$2x - \frac{3}{5} = x + \frac{1}{2}.$$

Accepted Answer

$$x = \frac{11}{10}$$

Question 8

Which of the following is the equation of the line with slope $$4$$ and $$y-$$intercept $$-2$$?

Accepted Answer

$$y = 4x - 2$$

Question 9

Solve the inequality $$3 \leq 2x + 1 \u003c 9.$$

Accepted Answer

$$1 \leq x \u003c 4$$

Question 10

Solve the absolute value equation $$|2x - 1| = 5.$$

Accepted Answer

$$x = 3 or$$ $$x = -2$$

Question 11

Which of the following is the factored form of $$x^2 - 9$?

Accepted Answer

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

Question 12

If $$|x - 2| \u003e 4$$, what is the solution set?

Accepted Answer

$$x  6$$

Question 13

Simplify $$\frac{6x^2$ + 9x}{3x}$$, assuming $$x 
eq 0.$$

Accepted Answer

$$2x + 3$$

Question 14

Find the $$x- $$and $$y-$$intercepts of $$2x + y = 4.$$

Accepted Answer

$$x-$$intercept: $$2$$, $$y-$$intercept: $$4$$

Question 15

Solve the system: $$\begin{cases} x + y = 5 \ 2x - y = 1 \end{cases}.$$

Accepted Answer

$$x = 2, y = 3$$

Question 16

Which of the following is the solution to $$|x| \leq 3$$?

Accepted Answer

$$-3 \leq x \leq 3$$

Question 17

Simplify $$3x - \frac{2}{4} - x + \frac{6}{2}.$$

Accepted Answer

$$2x + 2$$

Question 18

Which of the following is the correct solution to $$|3x + 2| = 2x + 8$$?

Accepted Answer

$$x = 6$$

Question 19

If $$y \u003e 2$$, which of the following graphs represents the solution set?

Accepted Answer

A shaded region above the line $$y = 2 ($$not including the line)

Question 20

Which of the following is the correct simplification of $$(2x - 3y) - (4x + y) + 5(3y - x)$$?

Accepted Answer

$$-3x + 11y$$

College Algebra Exam 1 Study Guide – Step-by-Step Guidance

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