Chapter 6

Linear Equations

100

Solve

4x+9=33

6

200

Simplify

3(4y-5) - (7y-2)

5y - 13

300

Solve

3/x=15/25

x=5

400

Solve for x

7x + 13 = 2(2x - 5) + 3x + 23

Infinitely many solutions

500

Solve for x

2x/3 = x/6 +1

x = 1/3

Linear Inequalities

100

Solve for x

2x - 5 < 3

x < 4

200

Solve for x

3 - 5x < 18

x > -3

300

4x + 3(2x - 7) < x - 3

x < 2

400

-1 < 4x + 2 < 6

-3/4 < x < 1

500

Create and solve the inequality: A widget factory has a fixed operating cost of $3,600 per day plus costs $1.40 per widget produced. If a widget sells for $4.20, what is the least number of widgets that must be sold per day to make a profit? 

1285 widgets

Quadratic Equations

100

Multiply these binomials 

(x + 9)(x - 5)

x²+ 4x - 45

200

Factor x² - x - 12

(x - 4)(x + 3)

300

Factor 3x² - 17x + 10

(x - 5)(3x - 2)

400

Solve

x² - 4x = 32

{-4, 8}

500

Solve 2x² + 5x - 3 = 0

{-3, 1/2}

Applications

100

A salesperson earns $300 per week plus 5% commission 

on sales. How much must be sold to earn $800 in a 

week

$10,000

200

After a 20% price reduction, an eReader sold for $96. What 

was the eReader’s price before the reduction?

$120

300

To determine the number of trout in a lake, a conservationist 

catches 112 trout, tags them, and returns them to the lake. 

Later, 82 trout are caught, and 32 of them are found to be 

tagged. How many trout are in the lake?

287 trout

400

The average yearly earnings of computer engineering 

majors exceeds the earnings of marketing majors by 

$23  thousand. The average yearly earnings of real estate 

majors exceeds the earnings of marketing majors by 

$6  thousand. Combined, the average yearly earnings for 

these three fields of study are $173  thousand. Determine 

the average yearly earnings, in thousands of dollars, for 

each of these three fields of study.

Marketing = 48K

Real Estate = 54K

Computer Engineering = 71K

500

To pass a course, a student must have an average on three 

examinations of at least 60. If a student scores 42 and 74 on 

the first two tests, what must be earned on the third test to 

pass the course?

64

Miscellaneous

100

Solve x/2 > -4

x > -8

200

Multiply

(4x - 7)(3x + 2)

12x² - 13x - 14

300

Solve for h: A + 3 = 1/2 bh - 5

h=(2A + 16)/b

400

Solve x² + 11x + 2 = 0

(-11 + sqrt(113))/2

500

Solve

(5x+1)(x+3) = 3(x - 4) + 7

{-8/5, -1}