Deck 1: Linear Equations and Inequalities in One Variable

Question 1

Solve the equation: 0.7(x - 10) + 0.5 = 1 - 0.6(20 - 2x) - 0.5.

A) x = 0.10
B) No solution
C) x = 10
D) x = 0

Answer 1

C

Question 2

Answer 2

B

Question 3

Write the word or phrase that best completes each statement or answers the question.
Solve the equation: 0.12 + 0.03(y - 5) = -0.01(y - 4) + 0.02.

Answer 3

Question 4

Solve the equation: -5(2y + 3) + 5 = 40.

Question 5

Which of the following is a linear equation?

Question 6

Write the word or phrase that best completes each statement or answers the question.
Solve the equation:

Question 7

Write the word or phrase that best completes each statement or answers the question.
Solve the equation: y + 5 = 7.

Question 8

Two numbers that differ by 19 have a sum of 53. Find the smaller of the two numbers.

A) 0
B)
C) 17
D) 19

Question 9

Solve the equation:

Question 10

Solve the equation: 6 - 3(-2 - 4x) = 2(3(x - 4) + 7).

Question 11

Solve the equation:

A) x = -4
B) x = 4
C) x = 0
D) No solution

Question 12

Write the word or phrase that best completes each statement or answers the question.
Solve the equation: -

Question 13

Use substitution to determine which value is the solution to 5x + 3 = 18.

A) x = 2
B) x = 9
C) x = 3
D) x = 1

Question 14

Solve the equation: 2(-3 - 3x) = 24.

Question 15

Use substitution to determine which value is the solution to -9y - 8 = 19.

A) x = -5
B) x = -3
C) x = -4
D) x = -19

Question 16

Question 17

Write the word or phrase that best completes each statement or answers the question.
Solve the equation: -3x + 8 = 7.

Question 18

Is the equation conditional, an identity, or a contradiction? 22y + 2(3 - y) = 5 + 20y + 2

A) Contradiction
B) Conditional
C) Identity

Question 19

Is the equation conditional, an identity, or a contradiction? y - 5 + 3y = 7y + 4

A) Identity
B) Contradiction
C) Conditional

Question 20

Is the equation conditional, an identity, or a contradiction?

A) Conditional
B) Contradiction
C) Identity

Question 21

A freight train and a passenger train leave a rail yard at the same time and travel on parallel tracks. The passenger train travels 6 mph faster than the freight train. The combined distance traveled after
2 hours is 100 miles. What is the average speed of each train?

A) 22 mph; 28 mph
B) 24 mph; 30 mph
C) 21 mph; 27 mph
D) 19 mph; 25 mph

Question 22

The sum of two consecutive integers is -75. Find the least of the two integers.

A) -76
B) 38
C) -37
D) -38

Question 23

One fruit punch has 45% fruit juice and another is 90% fruit juice. How much of the 45% punch should be mixed with 10 gal of the 90% punch to create a fruit punch that is 50% fruit juice?

A) 85 gal
B) 75 gal
C) 70 gal
D) 80 gal

Question 24

If t represents a number, write an expression for 7 less than twice the number.

A) 2t - 7
B) 2t + 7
C) 7 - 2t
D) 2(t - 7)

Question 25

A salesperson earns $60 a day plus 12% commission on sales over $200. If her daily earnings are $95.88, how much money in merchandise did she sell?

A) $559.00
B) $499.00
C) $680.91
D) $999.00

Question 26

Write the word or phrase that best completes each statement or answers the question.
If $15,000 is borrowed at 5.4% simple interest for 10 years, how much interest will be paid for the
loan?

Question 27

A car dealership marks up all new automobiles by 15%. What was the original wholesale cost of a car with a sticker price at this dealership of $22,500? Round your answer to the nearest cent.

A) $19,565.22
B) $25,875.00
C) $3,375.00
D) $18,700.00

Question 28

What is the sale price of a stereo that normally sells for $210.00 and is on sale for 25% off?

A) $157.50
B) $185.00
C) $262.50
D) $52.50

Question 29

The length of a rectangular plot of land is 3 times the width. If the perimeter is 1500 feet, find the dimensions of the plot. Round your answer to the nearest tenth, if necessary.

A) 750 ft × 2250 ft
B) 187.5 ft × 562.5 ft
C) 375 ft × 1125 ft
D) 100 ft × 300 ft

Question 30

Write the word or phrase that best completes each statement or answers the question.
For the fiscal year 2000, stock in giveusmoney.com gained 23%, while stock in Milton Steel
increased by 8%. An investor bought a combined total of $6000 of stock in these companies at the
beginning of the year, and made a profit of $600. How much was invested in each company?
Round your answers to the nearest cent.

Question 31

The sum of two numbers is 72. The larger number is 3 less than 3 times the smaller number. Find the smaller number.

Question 32

Two times the sum of three consecutive odd integers is the same as 25 more than 5 times the largest integer. Find the integers.

A) 37, 39, and 41
B) 25, 27, and 29
C) 33, 35, and 37
D) 29, 31, and 33

Question 33

Write the word or phrase that best completes each statement or answers the question.
A plot of land in the shape of an isosceles triangle will be used for an outdoor concert venue. The
sides that are equal in length will be twice as long as the third side; the perimeter will be 450 yards.
Find the dimensions.

Question 34

How many gallons of gasoline that is 6% ethanol must be added to 2,000 gallons of gasoline with no ethanol to get a mixture that is 4% ethanol?

A) 8000 gallons
B) 1,800 gallons
C) 5115 gallons
D) 4000 gallons

Question 35

Two cars are 270 miles apart and travel toward each other on the same road. They meet in 3 hours. One car travels 2 mph faster than the other. What is the average speed of each car?

A) 41 mph; 43 mph
B) 43 mph; 45 mph
C) 44 mph; 46 mph
D) 42 mph; 44 mph

Question 36

The tax rate on a used car in Overshoe County is 7%. What is the sales tax on a sport utility with a selling price of $15,000?

A) $1050.00
B) $10,500.00
C) $13,950.00
D) $525.00

Question 37

After his annual review, Miguel's salary was increased from $32,000 per year to $35,000. What percent increase does this represent? Round your answer to the nearest tenth of a percent.

A) 9.4%
B) 91.4%
C) 8.6%
D) 3000%

Question 38

Donna invested money in two accounts: one paying 4% simple interest and the other paying 3% simple interest. She invested $3000 more in the 4% account than in the 3% account. If she received
$960 in interest at the end of 1 yr how much did she invest in each account?

A) $14,000 at 4% and $11,000 at 3%
B) $11,000 at 4% and $14,000 at 3%
C) $12,000 at 4% and $15,000 at 3%
D) $15,000 at 4% and $12,000 at 3%

Question 39

The plans for a rectangular deck call for the width to be 10 feet less than the length. Sam wants the deck to have an overall perimeter of 60 feet. What should the length of the deck be?

A) 20 feet
B) 10 feet
C) 35 feet
D) 30 feet

Question 40

The sum of two consecutive even integers is 158. Find the least of the two integers.

A) 156
B) -78
C) 80
D) 78

Question 41

Solve for the indicated variable.

Question 42

Solve for x and then use its value to find the measure of each angle.

Question 43

Question 44

Solve for the indicated variable.

Question 45

Write the word or phrase that best completes each statement or answers the question.

Question 46

Solve for the indicated variable.

Question 47

One end of a stiff spring is attached firmly to the ceiling of a workshop (see figure). The load F (in pounds) required to stretch the spring by x inches is given by F = kx, where k is the stiffness constant
Of the spring. a. Solve F = kx for x.
B) How far will the spring stretch if its stiffness constant is 5 lb/in and it is loaded with a weight of
25)5 lb? Round to the nearest tenth of an inch.

Question 48

The mass of an object is equal to its density times its volume, or m = DV.

Question 49

Express the equation in the form y = mx + b by solving for y.

Question 50

Solve for F.

Question 51

Write the word or phrase that best completes each statement or answers the question.
Solve for x, and then find the measures of the two angles. (Figure is not necessarily drawn to scale.)

Question 52

Solve for x and then use its value to find the measure of each angle.

Question 53

Two angles are complementary. The larger of the two is 3° more than twice the smaller. Find the 2 angles.

A) 29° and 61°
B) 87° and 3°
C) 31° and 59°
D) 59° and 121°

Question 54

Solve for the indicated variable.

Question 55

Express the equation in the form y = mx + b by solving for y.

Question 56

Solve for the indicated variable.

Question 57

Solve for x and then use its value to find the measure of each angle.

Question 58

Question 59

Angles A, B, and C are the angles in a triangle. Angle B is 2 times as big as angle A, and angle C is 48° more than angle A. Find the measure of angle A in degrees.

A) 81°
B) 10.5°
C) 33°
D) 66°

Question 60

Solve for the indicated variable.

Question 61

Solve the inequality. Graph the solution set and write the solution set in interval notation. 13y + 6 > 8

Question 62

Question 63

Write the word or phrase that best completes each statement or answers the question.

Question 64

Solve the inequality. Write the solution set in interval notation.

Question 65

Solve the inequality. Write the solution set in interval notation.

Question 66

Solve the inequality. Graph the solution set and write the solution set in interval notation.

Question 67

Write the word or phrase that best completes each statement or answers the question.
Solve the inequality. Graph the solution set and write the solution set in interval notation.

Question 68

Solve the inequality. Graph the solution set and write the solution set in interval notation.

Question 69

Solve the inequality. Write the solution set in interval notation.

Question 70

Write the word or phrase that best completes each statement or answers the question.
Sparky has scores of 70, 67, and 73 on his first three Sociology tests. If he needs to keep an average
of 70 to stay eligible for lacrosse, what scores on the fourth exam will accomplish this?

Question 71

Solve the inequality. Write the solution set in interval notation.

Question 72

A rental company charges a flat fee of $7 to rent a power washer, plus $4 per day. How many days
could you keep the power washer if you plan to spend no more than $34?

Question 73

The revenue R for selling x fleece jackets is given by the equation R = 49.95x. The cost C (in dollars) to produce x jackets is C = 2600 + 15.50x. Find the number of jackets that the company
Needs to sell to produce a profit. (Hint: A profit occurs when revenue exceeds cost.)

A) More than 75
B) More than 76
C) At least 74
D) At least 75

Question 74

Question 75

Question 76

Question 77

Question 78

Question 79

Solve the inequality. Write the solution set in interval notation.

Question 80

Solve the inequality. Graph the solution set and write the solution set in interval notation.