Question 1

Distribute and simplify the expression $$-3(2x + y - 5). $$Which of the following is the correct result?

Accepted Answer

$$-6x - 3y + 15$$

Question 2

Combine like terms in the expression $$3x - 2y - x + 5 - 7 + 4y + 2x - 2. $$What is the simplified form?

Accepted Answer

$$4x + 2y - 4$$

Question 3

Solve for $$x in $$the equation $$3x + 2 = 7.$$

Accepted Answer

$$x = \, 5/3$$

Question 4

What is the least common denominator (LCD) of $$\frac{1}{6}$$, $$\frac{1}{8}$$, and $$\frac{1}{12}$$?

Accepted Answer

$$24$$

Question 5

Expand and simplify $$(x + 2)(x - 5). $$Which of the following is correct?

Accepted Answer

$$x^2 - 3x - 10$

Question 6

Solve for $$x in $$the equation $$\frac{2}{x} = \frac{5}{2}.$$

Accepted Answer

$$x = \frac{4}{5}$$

Question 7

Find the $$x- $$and $$y-$$intercepts of the line $$2x + 3y = 12.$$

Accepted Answer

$$x-$$intercept: $$6$$, $$y-$$intercept: $$4$$

Question 8

Write the equation $$y - 3 = 5(x + 1) in $$slope-intercept form.

Accepted Answer

$$y = 5x + 8$$

Question 9

Which of the following is the equation of the line passing through $$(2, -1)$$ and $$(2, 5)$$?

Accepted Answer

$$x = 2$$

Question 10

Determine if the system $$\begin{cases} 2x - 3y = 7 \ 6x - 9y = 21 \end{cases} is $$dependent, independent, or inconsistent.

Accepted Answer

Dependent

Question 11

Solve the system of equations: $$\begin{cases} x - 3y = -5 \ y = 4 \end{cases}.$$

Accepted Answer

$$x = 7,\ y = 4$$

Question 12

Solve the equation $$3(x - 1) + 2(3x - 5) = 5(2x + 3)$$ for $$x.$$

Accepted Answer

$$x = 2$$

Question 13

Write the equation $$5x - 3y = 30 in $$slope-intercept form.

Accepted Answer

$$y = \frac{5}{3}x - 10$$

Question 14

Solve the rational equation $$\frac{1}{3x} + \frac{2}{x + 1} = \frac{1}{6x}$$ for $$x ($$excluding extraneous solutions).

Accepted Answer

$$x = -2$$

Question 15

A chemist mixes two solutions: one with a concentration of $$x$$ and another with a concentration of $$x+2. If $$the total volume is $$2x+1$$ and the chemist wants to simplify $$\frac{2x(x+2)(2x+1)}{2x+1}$$, what is the result?

Accepted Answer

$$2x(x+2)$$

Question 16

Given the system $$\begin{cases} 2x - 3y = 7 \ 6x + 9y = 21 \end{cases}$$, what type of system is this?

Accepted Answer

Independent

Question 17

Solve the system $$\begin{cases} 2x - 3y = 3 \ 2x + 3y = 9 \end{cases}.$$

Accepted Answer

$$x = 3,\ y = 2$$

Question 18

A line passes through the points $$(-2, 3)$$ and $$(3, -1). $$What is the slope of this line?

Accepted Answer

$$-\frac{4}{5}$$

Question 19

Solve the rational equation $$\frac{1}{x+2} + \frac{2}{x-1} = \frac{3}{x}$$ for $$x ($$excluding extraneous solutions).

Accepted Answer

$$x = 2$$

Question 20

A medical researcher is analyzing the intersection of two dosage-response lines: $$3x + 4y = 5$$ and $$2x + 3y = 11. $$What is the solution $$(x, y) to $$this system?

Accepted Answer

$$x = -7,\ y = 9$$

Intermediate Algebra Exam 1 Review – Step-by-Step Guidance

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