Deck 2: Linear Equations and Inequalities

Question 1

Find an equation that has x=6 as a solution.

A) $- 2 x + 3 = - 5 ( x - 9 )$
B) $- 2 x + 3 = 5 ( x - 9 )$
C) $2 x + 3 = - 5 ( x - 9 )$
D) $2 x - 3 = - 5 ( x + 9 )$
E) $2 x + 3 = 5 ( x - 9 )$

Answer 1

$2 x + 3 = - 5 ( x - 9 )$

Question 2

Solve the linear equation $11 x - 5 = 11 - 5 x$ for x .

A) x=1
B) x=0
C) x=5
D) x=11
E) x=14

Answer 2

x=1

Question 3

Find an equation that has $x = - 3$ as a solution.

A) $5 x + 7 = - 8$
B) $- 5 x - 7 = - 8$
C) $5 x - 7 = - 8$
D) $5 x + 7 = 8$
E) $- 5 x + 7 = - 8$

Answer 3

$5 x + 7 = - 8$

Question 4

Solve the linear equation $7 x - 5 = 37$ for x .

A) x=-192
B) x=100
C) x=6
D) x=-53
E) x=-66

Question 5

Determine if $2 x - 7 = 3 x$ is a conditional equation, an identity equation, or an equation with no solution.

A) $\text { conditional equation }$
B) $\text { equation with no solution }$
C)identity equation

Question 6

Solve $6 y - 2 = 6 y$ , if possible.

A) y=-25
B) y=0
C) y=10
D) y=-16
E)no solution

Question 7

Solve the linear equation $7 x + 77 = 0$ for x .

A) x=-11
B) x=11
C) x=70
D) x= 55
E) x=1

Question 8

Solve the linear equation $4 ( x + 2 ) = - 9 ( x - 4 )$ for x .

A) $x = - \frac { 28 } { 13 }$
B) $x = \frac { 44 } { 13 }$
C) $x = - \frac { 44 } { 13 }$
D) x=0
E) $x = \frac { 28 } { 13 }$

Question 9

Solve the linear equation $7 x + 6 = - 4 ( x - 5 )$ for x .

A) $x = - \frac { 26 } { 11 }$
B) $x = \frac { 26 } { 11 }$
C) $x = \frac { 14 } { 11 }$
D) $x = - \frac { 14 } { 11 }$
E) x=0

Question 10

Solve the linear equation $- 7 ( y + 4 ) = - y + 2$ for y .

A) y=11
B) y=-10
C) y=0
D) y=5
E) y=-5

Question 11

Solve the linear equation $5 - 7 t = - 19 + t$ for t .

A) t=3
B) t=-16
C) t=-3
D) t=16
E) t=0

Question 12

Solve the equation $x + 9 = 26$ .

A) x=234
B) x=17
C) x=-17
D) x=-234
E) x=0

Question 13

Determine if x=2 is a solution to $x + 8 = 3 x$ .

A) x=2 is a solution.
B) x=2 is not a solution.

Question 14

Solve the linear equation $- 6 - 2 x = 6$ for x .

A) x=-6
B) x=66
C) x=-100
D) x=55
E) x=10

Question 15

Solve the equation $6 x = 48$ .

A) $x = 54$
B) x=42
C) x=24
D) x=62
E) x=8

Question 16

Determine if x=-3 is a solution to $x + 16 = - 3 x$ .

A) x=-3 is not a solution.
B) x=-3 is a solution.

Question 17

Find an equation that has $x = - \frac { 21 } { 4 }$ as a solution.

A) $2 x + 5 = - 2 ( x + 8 )$
B) $- 2 x + 5 = - 2 ( x + 8 )$
C) $2 x + 5 = 2 ( x + 8 )$
D) $2 x - 5 = - 2 ( x - 8 )$
E) $- 2 x + 5 = 2 ( x + 8 )$

Question 18

Determine whether the equations $8 ( 10 - 5 t ) = 2$ and $80 - 40 t = 2$ are equivalent.

A)not equivalent
B)equivalent

Question 19

Solve the equation $x - 7 = 5$ .

A) x=35
B) $x = - \frac { 5 } { 7 }$
C) x=2
D) x=12
E) x=22

Question 20

Determine whether the equations $x + 8 = 13$ and $2 x + 24 = 26$ are equivalent.

A)not equivalent
B)equivalent

Question 21

Solve the equation $\frac { x } { 6 } = 5$ .

A) $x = \frac { 5 } { 6 }$
B) x=11
C) $x = \frac { 6 } { 5 }$
D) x=30
E) x=-1

Question 22

Two people can complete a task in t hours, where t must satisfy the equation $$\frac { t } { 25 } + \frac { t } { 30 } = 1$$ . Find the required time t , in hours. Round your answer to two decimal places.

A) $2.20$ hours
B) $13.64$ hours
C) $150.00$ hours
D) $55.00$ hours
E)no solution

Question 23

Complete the table showing the equivalent forms of a percent. Reduce fractions to simplest form. Percent Parts out of 100 Decimal Fraction $\frac { 3 } { 10 }$

A) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts out of } 100 & \text { Decimal } & \text { Fraction } \\\hline 3 \% & 3 & 0.03 & \frac { 3 } { 10 } \\\hline\end{array}$ .

B) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts out of } 100 & \text { Decimal } & \text { Fraction } \\\hline 30 \% & 3.33 & 0.3 & \frac { 3 } { 10 } \\\hline\end{array}$

C) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts out of } 100 & \text { Decimal } & \text { Fraction } \\\hline \frac { 3 } { 10 } \% & 3 & 0.3 & \frac { 3 } { 10 } \\\hline\end{array}$

D) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts out of } 100 & \text { Decimal } & \text { Fraction } \\\hline 30 \% & 30 & 0.3 & \frac { 3 } { 10 } \\\hline\end{array}$ .

E) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts out of } 100 & \text { Decimal } & \text { Fraction } \\\hline 30 \% & 30 & 0.3 & \frac { 3 } { 10 } \\\hline\end{array}$

Question 24

Write $" 36 \text { inches to } 54 \text { inches" }$ as a ratio and simplify.

A) $\frac { 1 } { 36 }$
B) $- \frac { 1 } { 3 }$
C) $\frac { 5 } { 3 }$
D) $\frac { 3 } { 2 }$
E) $\frac { 2 } { 3 }$

Question 25

What number is 150% of 38?

A)1.5
B)0.38
C)67
D)5.7
E)57

Question 26

The perimeter of a rectangle is $216$ inches. The length of the rectangle is $\text { three }$ times its width. Find the dimensions of the rectangle.

A)length: $54$ inches width: $162$ inches
B)length: $162$ inches width: $54$ inches
C)length: $81$ inches width: $27$ inches
D)length: $27$ inches width: $81$ inches
E)length: $108$ inches width: $36$ inches

Question 27

Complete the table showing the equivalent forms of a percent. Reduce fractions to simplest form. Percent Parts out of 100 Decimal Fraction 65%

A) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts out of } 100 & \text { Decimal } & \text { Fraction } \\\hline 65 \% & 65 & 0.65 & \frac { 13 } { 20 } \\\hline\end{array}$
B) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts out of } 100 & \text { Decimal } & \text { Fraction } \\\hline 65 \% & 0.65 & 1.54 & \frac { 65 } { 100 } \\\hline\end{array}$
C) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts aut of } 100 & \text { Decimal } & \text { Fraction } \\\hline 65 \% & 65 & 0.02 & \frac { 1 } { 65 } \\\hline\end{array}$
D) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts out of } 100 & \text { Decimal } & \text { Fraction } \\\hline 65 \% & 65 & 0.02 & \frac { 13 } { 20 } \\\hline\end{array}$
E) $\begin{array} { | c | c | c | c | } \hline \text { Percent } & \text { Parts out of } 100 & \text { Decimal } & \text { Fraction } \\\hline 65 \% & 1.54 & 0.65 & \frac { 65 } { 100 } \\\hline\end{array}$

Question 28

The sum of 5 consecutive odd integers is 305 . Find the 5 integers.

A) $57,59,61,63,65$
B) $53,57,61,65,69$
C) $56,58,60,62,64$
D) $59,60,61,62,63$
E) $59,61,63,65,67$

Question 29

You have a job on an assembly line for which you are paid $12 per hour plus $0.50 per unit assembled. Write an algebraic model to find the number of units produced in an eight-hour day if your earnings for the day are $144 and then solve the resulting algebraic equation. Round your solution to the nearest integer.

A)equation: $0.50 x - ( 12 ) = 144$ solution: 240
B)equation: $0.50 x - 8 ( 12 ) = 144$ solution: 1
C)equation: $8 ( 12 ) + x = 144$ solution: 48
D)equation: $8 ( 12 ) + 0.50 x = 144$ solution: 96
E)equation: $x - 8 ( 12 ) = 144$ solution: $9$

Question 30

Solve the linear equation $6 ( y + 3 ) = 8 y - 2 y + 6$ for y .

A) y=1
B) y=9
C) y=5
D) y=0
E)no solution

Question 31

Solve the proportion $\frac { x } { 5 } = \frac { 7 } { 20 }$ to determine x .

A) x= $\frac { 7 } { 100 }$
B) $x = 2$ 7
C) x= - $\frac { 7 } { 100 }$
D) x=21
E) x= $\frac { 7 } { 4 }$

Question 32

1645.6 is 88% of what number?

A)1880
B)1,448
C)1852
D)1899
E)1870

Question 33

The perimeter of a rectangle is $180$ inches. The length of the rectangle is $\text { four }$ times its width. Find the area of the rectangle.

A) $5,184$ square inches
B) $2,592$ square inches
C) $5,508$ square inches
D) $1,296$ square inches
E) $720$ square inches

Question 34

The bill for repairing a car was $\$ 330$ . The cost for parts was $\$ 155$ . The cost for labor was $\$ 25$ per hour. How many hours did the repair work take?

A) $7$ hours
B) $14$ hours
C) $2$ $\text { hours }$
D) $13$ hours
E) $9$ hours

Question 35

Solve $1.2 ( x - 5 ) = 14.4$ , if possible.

A) x=3.8
B) x=10.6
C) x=8
D) x=17
E)no solution

Question 36

Solve the linear equation $\frac { 1 } { 4 } x + 2 = \frac { 6 } { 7 } x - 3$ for x .

A) $x = \frac { 140 } { 17 }$
B) $x = - \frac { 140 } { 17 }$
C) $x = \frac { 28 } { 17 }$
D) $x = - \frac { 28 } { 17 }$
E)there is no solution

Question 37

What number is 8% of 1236?

A)989
B)0.06
C)154.5
D)98.88
E)9,888

Question 38

The sum of four consecutive odd integers is 216. Find the four integers.

A) $54,53,55,57$
B) $53,55,57,51$
C) $50,53,55,57$
D) $51,53,55,57$
E) $52,53,55,57$

Question 39

2.7 is what percent of 482? Round your answer to two decimal places.

A)0.56 %
B)178.52 %
C)1.30 %
D)13.01 %
E)5.60 %

Question 40

Solve the linear equation $- \frac { 1 } { 3 } = \frac { 1 } { 10 }$ for t .

A) $t = \frac { 7 } { 30 }$
B) $t = \frac { 2 } { 13 }$
C) $t = - \frac { 3 } { 10 }$
D) $t = \frac { 13 } { 30 }$
E) $t = - \frac { 2 } { 13 }$

Question 41

A shoe store sells a pair of athletic shoes for . The shoes go on sale for . What is the discount?

A)
B)
C)
D)
E)

Question 42

If a product has a cost of $738 and a markup rate of $\$ 32 \frac { 1 } { 3 } \%$ , what is the markup?

A) $\$ 249.07$
B) $\$ 238.62$
C) $\$ 236.16$
D) $\$ 263.18$
E) $\$ 246.00$

Question 43

The floor of a rectangular room that measures 10 feet by 12 feet is partially covered with a circular rug with a radius of 4 feet (see figure). What percent of the floor is covered by the rug? Round your answer to the nearest integer.

$a = 10 , b = 12$

A)46%
B)42%
C)10%
D)21%
E)58%

Question 44

Find the unit price (in dollars per ounce)if a 1-pound, 14-ounce loaf of bread costs $1.80.

A)$0.08 per ounce
B)$0.13 per ounce
C)$0.09 per ounce
D)$0.06 per ounce
E)$0.11 per ounce

Question 45

Solve the proportion $\frac { 5 x + 3 } { 9 } = \frac { 9 - 2 x } { 4 }$ to determine x .

A) x= $\frac { 93 } { 38 }$
B) x= $\frac { 69 } { 38 }$
C) x= $- \frac { 3 } { 19 }$
D) x= $- \frac { 3 } { 38 }$
E) x= $\frac { 39 } { 19 }$

Question 46

A tractor uses 6 gallons of diesel fuel to plow for 105 minutes. Determine the number of gallons of fuel used in 7 hours. Round your answer to two decimal places.

A)24.00 gallons
B)2.40 gallons
C)1.50 gallons
D)27.20 gallons
E)0.40 gallon

Question 47

Approximately 12% of the students enrolled at Penn State University in the fall of 2006 were freshmen. The total enrollment for the school in the fall of 2006 was 83,030. How many freshmen were enrolled? Round your answer to the nearest integer.

A)73,066
B)9,964
C)11,624
D)996
E)13,285

Question 48

Which is a better buy, a four ounce package of cookies for $1.68 or a six ounce package of cookies for $2.38?

A)The four ounce package is a better buy.
B)The six ounce package is a better buy.

Question 49

Use cross-multiplication to solve the equation $\frac { x - 3 } { 4 } = \frac { 19 } { 24 }$ for x .

A) x= - $\frac { 13 } { 6 }$
B) x= $\frac { 37 } { 6 }$
C) x= - $\frac { 1 } { 6 }$
D) x= $\frac { 13 } { 6 }$
E) x= $\frac { 1 } { 6 }$

Question 50

Find the unit price (in dollars per ounce)if a 15-ounce can of pineapple costs $3.45.

A)$0.30 per ounce
B)$0.28 per ounce
C)$0.25 per ounce
D)$0.23 per ounce
E)$0.26 per ounce

Question 51

A customer gave a taxi driver $24 for a ride that cost $18. Determine the tip rate. Round your answer to the nearest integer.

A)33%
B)75%
C)6%
D)36%
E)25%

Question 52

An item at a tourist shop sells for . The cost of the item to the shop is . What is the markup rate?

A)
B)
C)
D)
E)

Question 53

If a product has a cost of and a selling price of , what is the markup?

A)
B)
C)
D)
E)

Question 54

If a product has a cost of and a selling price of , what is the markup rate? Round your answer to two decimal places.

A)
B)
C)
D)
E)

Question 55

Solve for the length of x using the fact that corresponding sides of similar triangles are proportional. Round your answer to two decimal places. $\frac { | a + 8 | } { 2 } \geq 20$ $\{ a \mid a \leq - 48 \text { or } a \geq 32 \}$

A)1.30
B)10.40
C)6.15
D)4.06
E)1.60

Question 56

If a product has a cost of $730 and a markup rate of $\$ 30 \frac { 1 } { 3 } \%$ , what is the selling price?

A) $\$ 983.33$
B) $\$ 760.33$
C) $\$ 951.43$
D) $\$ 760.00$
E) $\$ 949.00$

Question 57

Solve the proportion $\frac { 3 } { 16 } = \frac { x } { 10 }$ .

A) x= $\frac { 7 } { 100 }$
B) x= $\frac { 7 } { 4 }$
C) x=- $\frac { 3 } { 10 }$
D) $x =$ $\frac { 15 } { 8 }$
E) $x =$ $\frac { 3 } { 10 }$

Question 58

If a product is discounted by $249.9 and is selling for $860.1 , what is the list price?

A) $\$ 1,120.45$
B) $\$ 610.20$
C) $\$ 1,104.60$
D) $\$ 1,110.00$
E) $\$ 1,134.56$

Question 59

If a product is discounted by $\$ 233.9$ and is selling for $\$ 890.1$ , what is the discount rate? Round your answer to two decimal places.

A) 15.41%
B) 26.28%
C) 20.81%
D) 35.64%
E) 79.19%

Question 60

A shoe store sells a pair of shoes for . The cost of the shoes to the store is . What is the markup?

A)
B)
C)
D)
E)

Question 61

Determine whether the inequalities $- 4 ( x + 10 ) > 8$ and $x + 10 > - 2$ are equivalent.

A)not equivalent
B)equivalent

Question 62

A free-falling object is described by $h = 35 t + \frac { 1 } { 2 } a t ^ { 2 }$ , where h is the height above the ground, t is the amount of time the object is falling, and a is the acceleration. Solve the equation for a .

A) $a = \frac { 2 ( h - 35 t ) } { t }$
B) $a = \frac { 2 ( h + 35 t ) } { t ^ { 2 } }$
C) $a = \frac { 2 ( h - 35 t ) } { t ^ { 2 } }$
D) $a = \frac { h - 35 t } { t ^ { 2 } }$
E) $a = \frac { h - 35 t } { 2 t ^ { 2 } }$

Question 63

If it takes you 12 hours to complete a job, what portion do you complete each hour?

A) 12%
B) 0.12
C) $\frac { 1 } { 12 }$
D) 11
E) 0.88

Question 64

A chemist wishes to mix a 30% acid solution with a 60% acid solution to obtain 60 quarts of a 39% acid solution. How many quarts of each solution should be mixed together?

A) 42 quarts of 30% solution 18 quarts of $60 \%$ solution
B) $36$ quarts of $30 \%$ solution $24$ quarts of $60 \%$ solution
C) $24$ quarts of $30 \%$ solution $36$ quarts of $60 \%$ solution
D) $30$ quarts of $30 \%$ solution $30$ quarts of $60 \%$ solution
E) $18$ quarts of $30 \%$ solution $42$ quarts of $60 \%$ solution

Question 65

Determine whether the inequalities $7 x - 2 \leq 5 x + 4$ and $2 x \leq 6$ are equivalent.

A)equivalent
B)not equivalent

Question 66

Two cars start at the same point and travel in the same direction at average speeds of 65 miles per hour and 40 miles per hour. How much time (in hours)must elapse before the two cars are 87.5 miles apart?

A) 3.5 hours
B) 3.49 hours
C) 1.35 hours
D) $0.83$ hour
E) $2.19$ hours

Question 67

Sketch the graph of $1 \leq x \leq 5$ .

A)
B)
C)
D)
E)

Question 68

Ticket sales for a spaghetti dinner total . There are four times as many adult tickets sold as children s tickets. The prices of the tickets for adults and children are and , respectively. Find the number of children s tickets sold.

A) children s tickets
B) children s tickets
C) children s tickets
D) children s tickets
E) children s tickets

Question 69

Which inequality has the graph that is shown?

A) $1 < x < 4$
B) $x < 4$
C) $x \geq 4$
D) $1 \leq x \leq 4$
E) $x \leq 4$

Question 70

Which of the following is a solution to the inequality $2 - ( x + 9 ) \geq 4$ ?

A) x=-15
B) x=-10
C) x=-8
D) x=4
E) x=0

Question 71

Solve the inequality: $x + 7 \leq - 2$

A) $x \geq - 9$
B) $x \leq - 9$
C) $x \leq 9$
D) $x \geq - 14$
E) $x \leq - \frac { 2 } { 7 }$

Question 72

A grocer wishes to mix two kinds of nuts costing $2.26 per pound and $3.93 per pound to make a 124 pounds of mixed nuts costing $2.36 per pound. To determine the number of pounds of the $2.26 per pound nuts in the mixture, solve for x in the equation $2.26 x + 3.93 ( 124 - x ) = 292.64$ . How many pounds of the $2.26 per pound nuts should be included in the mixture? Round to the nearest pound.

A) $7$ pounds
B) $62$ pounds
C) 5 pounds
D) $82$ pounds
E) $117$ pounds

Question 73

Determine if x=-6 satisfies $0 < \frac { x + 5 } { 6 } < 2$ .

A) x=-6 does satisfy the inequality.
B) x=-6 does not satisfy the inequality.

Question 74

The annual insurance premium for a policy holder was $837 . The policy holder must pay a 18% surcharge because of an accident. What is the new annual premium as a result of the accident?

A) $\$ 990.66$
B) $\$ 977.66$
C) $\$ 855.00$
D) $\$ 987.66$
E) $\$ 991.66$

Question 75

Which of the following is a solution to the inequality $5 - \frac { 1 } { 3 } x > 0$ ?

A) x=15
B) x=5
C) x=14
D) x=9
E) x=10

Question 76

Graph the inequality $x < - 2$ or $x \geq 1$ .

A)
B)
C)
D)
E)

Question 77

Solve: $2 x < 4$

A) $x < \frac { 1 } { 2 }$
B) $x < 2$
C) x=2
D) $x \leq 2$
E) $x > 2$

Question 78

Which inequality has the graph that is shown?

A) $1 \leq x < 4$
B) $1 < x \leq 4$
C) $1 \leq x \leq 4$
D) $1 \leq x \leq 6$
E) $1 < x < 4$

Question 79

Ticket sales for a play total . There are three times as many adult tickets sold as children s tickets. The prices of the tickets for adults and children are and , respectively. Find the number of children s tickets sold.

A) children s tickets
B) children s tickets
C) children s tickets
D) children s tickets
E) children s tickets

Question 80

Two airplanes leave Chicago's O'Hare International Airport at the same time and fly in opposite directions. How far apart are the planes after $2 \frac { 1 } { 3 }$ hours if their average speeds are 450 miles per hour and 580 miles per hour? Round your answer to two decimal places.

A) $2,403.33$ miles
B) $1,353.33$ miles
C) $2,060.00$ miles
D) $1,050.00$ miles
E) $1,030.00$ miles