Question 1

Distribute to eliminate the parentheses in the expression $$-3(2x + y - 5). $$What is the simplified result?

Accepted Answer

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

Question 2

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

Accepted Answer

$$4x + 2y - 4$$

Question 3

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

Accepted Answer

$$x = \, rac{5}{3}$$

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 the expression $$(x + 2)(x - 5). $$What is the result?

Accepted Answer

$$x^2 - 3x - 10$

Question 6

Solve for $$x in $$the equation $$2x = 5.$$

Accepted Answer

$$x = 2.5$$

Question 7

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

Accepted Answer

$$x-$$intercept: $$(6, 0)$$, $$y-$$intercept: $$(0, 4)$$

Question 8

Write the equation of the line through the points $$(2, -1)$$ and $$(2, 5). $$What is the equation?

Accepted Answer

$$x = 2$$

Question 9

Determine if the system of equations is dependent, independent, or inconsistent:

$$\begin{cases} 2x - 3y = 7 \ 6x - 9y = 21 \end{cases}$$

Accepted Answer

Dependent

Question 10

Solve the system of equations:

$$\begin{cases} x - 3y = -5 \ y = 4 \end{cases}$$

What is the value of $$x$$?

Accepted Answer

$$x = 7$$

Question 11

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

Accepted Answer

$$x = 4$$

Question 12

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

Accepted Answer

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

Question 13

Solve the rational equation $$\frac{1}{x + 2} + \frac{2}{x - 1} = \frac{3}{x}. $$What is a valid solution for $$x$$?

Accepted Answer

$$x = 2$$

Question 14

Given the line $$y - 3 = 5(x + 1)$$, what is the slope-intercept form?

Accepted Answer

$$y = 5x + 8$$

Question 15

Determine if the system is dependent, independent, or inconsistent:

$$\begin{cases} 2x - 3y = 7 \ 6x - 9y = 10 \end{cases}$$

Accepted Answer

Inconsistent

Question 16

Solve the rational equation $$\frac{1}{3x} + \frac{2}{x + 1} = \frac{1}{6x}. $$What is a valid solution for $$x$$?

Accepted Answer

$$x = 2$$

Question 17

Write the equation of the line through $$(2, -1)$$ and $$(5, -1). $$What is the equation?

Accepted Answer

$$y = -1$$

Question 18

Solve the system of equations:

$$\begin{cases} 2x - 3y = 3 \ 2x + 3y = 9 \end{cases}$$

What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 19

A chemist mixes two solutions, one with a concentration of $$x$$ and another with a concentration of $$x + 2. If $$the total concentration after mixing is $$2x + 1$$, which expression represents the simplified form of $$2x(x + 2)(2x + 1) / (2x + 1)$$?

Accepted Answer

$$2x(x + 2)$$

Question 20

A business finds that its profit $$P (in $$thousands of dollars) can be modeled by $$P = 3x^2$ + 2x - 1$$, where $$x is $$the number of units sold (in hundreds). If the profit equals $$3x^2 + 4x$, for what value of x$ does this occur?

Accepted Answer

$$x = -0.5$$

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

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