Question 1

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

Accepted Answer

$$6x - 1$$

Question 2

Solve the linear equation for $$x$$: $$5x - 2 = 3x + 10.$$

Accepted Answer

$$x = 6$$

Question 3

Which of the following is the solution set for the inequality $$2x + 7 \u003c 15$$?

Accepted Answer

$$x \u003c 4$$

Question 4

A chemist needs to prepare a solution by mixing two chemicals. The cost of chemical A is \$$3 per liter and chemical B is \5 $$per liter. If the chemist wants to spend exactly \$$40 and use 10 liters in total, how many liters of chemical A should be used? (Let x$ be the liters of chemical A.)

Accepted Answer

Question 5

Which of the following is the equation of a line in standard form that passes through the points $$(2, 3)$$ and $$(4, 7)$$?

Accepted Answer

Question 6

A car rental company charges a base fee of \$$25 plus \0.20 $$per mile driven. Which equation models the total cost $$C$$ for driving $$m$$ miles?

Accepted Answer

$$C = 0.2m + 25$$

Question 7

Given the equation $$3x - 4y = 12$$, what is the $$y-$$intercept of the line?

Accepted Answer

$$(0, -3)$$

Question 8

Which of the following is the solution to the system of equations: $$x + y = 8$$ and $$2x - y = 1$$?

Accepted Answer

$$(3, 5)$$

Question 9

A line passes through the point $$(1, 2)$$ and has a slope of $$-3. $$Which of the following is its equation in point-slope form?

Accepted Answer

$$y - 2 = -3(x - 1)$$

Question 10

If $$f(x) = 2x + 5$$, what is $$f(3)$$?

Accepted Answer

$$11$$

Question 11

Which of the following best describes the graph of the equation $$y = -2x + 4$$?

Accepted Answer

A line with slope $$-2$$ and $$y-$$intercept $$4$$

Question 12

A business finds that its profit $$P (in $$dollars) from selling $$x$$ units is given by $$P = 50x - 200. $$What is the break-even point?

Accepted Answer

$$x = 4$$

Question 13

Which of the following is the solution to the inequality $$-3x + 9 \u003e 0$$?

Accepted Answer

$$x \u003c 3$$

Question 14

If the equation of a line is $$y = \frac{1}{2}x - 3$$, what is the slope and $$y-$$intercept?

Accepted Answer

Slope $$= \frac{1}{2}$$, $$y-$$intercept $$= -3$$

Question 15

A medical researcher is tracking the temperature $$T (in $$degrees Celsius) of a patient over time $$t (in $$hours) and finds that $$T = 37 - 0.5t. $$What is the patient's temperature after 6 hours?

Accepted Answer

$$34\ ^\circ\mathrm{C}$$

Question 16

Which of the following is the correct solution for $$4(x - 2) = 2x + 6$$?

Accepted Answer

$$x = 5$$

Question 17

A line has the equation $$2x + 3y = 12. $$What is the $$x-$$intercept?

Accepted Answer

$$(6, 0)$$

Question 18

If the cost to produce $$x$$ items is $$C = 7x + 120$$, what is the fixed cost?

Accepted Answer

$$120$$

Question 19

Which of the following is the solution to the system: $$y = 2x + 1$$ and $$y = -x + 7$$?

Accepted Answer

$$(2, 5)$$

Question 20

A company wants to model its revenue $$R (in $$dollars) as a function of the number of units sold $$n. If $$each unit sells for \$$15 and there is a fixed cost of \100$$, which equation represents the revenue?

Accepted Answer

$$R = 15n$$

Precalculus Study Guide: Algebraic Expressions, Linear Equations, and Graphing Lines

Study Guide - Practice Questions

Study Guide - Flashcards