Deck 8: A Transition From Elementary Algebra to Intermediate Algebra

Question 1

Solve the equation. $\frac { 2 x - 1 } { 4 } + \frac { 3 x + 2 } { 12 } = \frac { 5 } { 8 }$

A) $\left\{ \frac { 17 } { 18 } \right\}$
B) $\left\{ \frac { 18 } { 17 } \right\}$
C) $\left\{ - \frac { 18 } { 17 } \right\}$
D) $\left\{ - \frac { 17 } { 18 } \right\}$
E) $\varnothing$

Answer 1

$\left\{ \frac { 17 } { 18 } \right\}$

Question 2

The cross products in a proportion are equal.

Answer 2

True

Question 3

Solve the equation. $- 2 ( 3 x - 1 ) - 3 ( 2 x + 5 ) = - 5 ( 2 x - 8 )$

A) $\left\{ - \frac { 53 } { 2 } \right\}$
B) $\left\{ \frac { 53 } { 2 } \right\}$
C) $\left\{ - \frac { 49 } { 2 } \right\}$
D) $\left\{ \frac { 49 } { 2 } \right\}$
E) $\varnothing$

Answer 3

$\left\{ - \frac { 53 } { 2 } \right\}$

Question 4

Equivalent equations are equations that have the same solution set.

Question 5

Solve the equation. $- 5 = 7 x + 2$

A) $\{ 1 \}$
B) $\{ 2 \}$
C) $\{ - 1 \}$
D) $\{ - 2 \}$
E) $\varnothing$

Question 6

Desa invested a certain amount of money at 4% interest and $2,500 more than that amount at 7%. Her total yearly interest was $835. How much did she invest at each rate?

A) $7,000 at 4% and $9,500 at 7%
B) $8,500 at 4% and $6,000 at 7%
C) $6,000 at 4% and $8,500 at 7%
D) $5,000 at 4% and $7,500 at 7%
E) $8,000 at 4% and $10,500 at 7%

Question 7

Solve the equation. $9 ( 2 x + 3 ) = 7 ( 3 x - 2 )$

A) $\left\{ - \frac { 38 } { 3 } \right\}$
B) $\left\{ \frac { 38 } { 3 } \right\}$
C) $\left\{ \frac { 41 } { 3 } \right\}$
D) $\left\{ - \frac { 41 } { 3 } \right\}$
E) $\varnothing$

Question 8

The ratio of male students to female students at a certain university is 5 to 7. If there is a total of 15,840 students, find the number of male and the number of female students.

A) 6,700 males and 9,140 females
B) 6,700 males and 9,040 females
C) 6,800 males and 9,040 females
D) 6,600 males and 9,240 females
E) 9,240 males and 6,600 females

Question 9

The sum of the present ages of Eric and his father is 59 years. In 11 years, his father will be twice as old as Eric will be at that time. Find their present ages.

A) Eric is 14 and his father is 45 years old
B) Eric is 16 and his father is 43 years old
C) Eric is 15 and his father is 44 years old
D) Eric is 16 and his father is 45 years old
E) Eric is 13 and his father is 46 years old

Question 10

An algebraic equation is called a closed sentence.

Question 11

One leg of a right triangle is 4 meters shorter than the other leg. If the length of the hypotenuse is 20 meters, find the length of each leg.

A) 12 meters and 15 meters
B) 13 meters and 16 meters
C) 12 meters and 16 meters
D) 12 meters and 20 meters
E) 13 meters and 15 meters

Question 12

Solve the equation. $\frac { 2 } { 3 } x - \frac { 1 } { 2 } + \frac { 1 } { 4 } x = \frac { 5 } { 8 }$

A) $\left\{ \frac { 25 } { 22 } \right\}$
B) $\left\{ - \frac { 25 } { 22 } \right\}$
C) $\left\{ \frac { 27 } { 22 } \right\}$
D) $\left\{ - \frac { 27 } { 22 } \right\}$
E) $\varnothing$

Question 13

Solve the equation. $\frac { 2 x - 1 } { 3 } - \frac { 3 x + 2 } { 5 } = - 4$

A) $\{ - 51 \}$
B) $\{ - 47 \}$
C) $\{ - 49 \}$
D) $\{ 49 \}$
E) $\varnothing$

Question 14

Find three consecutive integers whose sum is $- 57$ .

A) $- 23 , - 22 , - 21$
B) $- 22 , - 21 , - 20$
C) $- 21 , - 20 , - 19$
D) $- 20 , - 19 , - 18$
E) $- 19 , - 18 , - 17$

Question 15

When an equation contains fractional forms, multiply both sides by the greatest common factor of all of the denominators.

Question 16

Solve the equation. $0.05 x - 5 ( x + 0.5 ) = 1.2$

A) $\left\{ - \frac { 26 } { 33 } \right\}$
B) $\left\{ \frac { 74 } { 99 } \right\}$
C) $\left\{ - \frac { 74 } { 99 } \right\}$
D) $\left\{ - \frac { 76 } { 99 } \right\}$
E) $\varnothing$

Question 17

There are 59 students in a certain class. The number of females is 5 less than three times the number of males. Find the number of females and the number of males in the class.

A) 16 males and 43 females
B) 44 males and 17 females
C) 43 males and 16 females
D) 44 males and 16 females
E) 17 males and 44 females

Question 18

Solve the equation. $\frac { x + 3 } { 3 } + 7 = \frac { x - 3 } { 3 }$

A) $\{ 10.5 \}$
B) $\{ - 9.5 \}$
C) $\{ - 10.5 \}$
D) $\{ 11.5 \}$
E) $\varnothing$

Question 19

Sean bought 5 lemons and 3 limes for $3.30. At the same prices, Kim bought 4 lemons and 7 limes for $4.25. Find the price per lemon and the price per lime.

A) $0.65 each for lemons and $0.55 each for limes
B) $0.35 each for lemons and $0.45 each for limes
C) $0.55 each for lemons and $0.45 each for limes
D) $0.45 each for lemons and $0.55 each for limes
E) $0.45 each for lemons and $0.35 each for limes

Question 20

Solve the equation. $8 - 3 x = 7 + 3 x$

A) $\left\{ - \frac { 1 } { 5 } \right\}$
B) $\left\{ \frac { 1 } { 5 } \right\}$
C) $\left\{ \frac { 1 } { 6 } \right\}$
D) $\left\{ \frac { 1 } { 7 } \right\}$
E) $\varnothing$

Question 21

Solve the system of equations. $\left( \begin{array} { l } 3 x - y = 6 \\6 x - 2 y = - 2\end{array} \right)$

A) $( 3 , - 3 )$
B) $( 3,3 )$
C) $( 1,3 )$
D) $( 1 , - 3 )$
E) no solution

Question 22

Solve the system of equations.

Question 23

Solve the equation.

Question 24

Solve the system of equations.

Question 25

Solve the equation.

Question 26

Solve the system of equations. $\left( \begin{array} { c } x - 2 y = 8 \\3 x + 7 y = - 15\end{array} \right)$

A) $( - 2,5 )$
B) $( 2 , - 4 )$
C) $( 2,3 )$
D) $( 2 , - 3 )$
E) $( 2 , - 5 )$

Question 27

Solve the system of equations.

Question 28

Solve the system of equations. $\left( \begin{array} { l } 3 x + 4 y = - 24 \\5 x - 7 y = - 40\end{array} \right)$

A) $( - 9,0 )$
B) $( 0 , - 8 )$
C) $( 9,0 )$
D) $( - 10,0 )$
E) $( - 8,0 )$

Question 29

Find three consecutive integers whose sum is . Please enter your answer as three numbers, separated by commas.

Question 30

The perimeter of a rectangle is 50 inches and its area is 144 square inches. Find the length and width of the rectangle. Width = __________ inches Length = __________ inches Please enter your answer as two numbers, separated by a comma.

Question 31

Solve the equation.

Question 32

Solve the equation.

Question 33

Solve the equation.

Question 34

Solve the equation.

Question 35

The perimeter of a rectangle is 46 inches and its area is 120 square inches. Find the length and width of the rectangle.

A) 10 inches by 17 inches
B) 8 inches by 15 inches
C) 9 inches by 17 inches
D) 8 inches by 16 inches
E) 9 inches by 16 inches

Question 36

Solve the equation.

Question 37

Solve the equation.

Question 38

Domenica and Javier start from the same location at the same time and ride their bicycles in opposite directions for 4 hours, at which time they are 128 miles apart. Domenica rides 4 miles per hour faster than Javier. Find the rate of each rider.

A) 13 miles per hour for Javier and 19 miles per hour for Domenica
B) 13 miles per hour for Javier and 17 miles per hour for Domenica
C) 14 miles per hour for Javier and 17 miles per hour for Domenica
D) 14 miles per hour for Javier and 18 miles per hour for Domenica
E) 15 miles per hour for Javier and 19 miles per hour for Domenica

Question 39

Solve the equation.

Question 40

Solve the equation.

Question 41

Solve the compound inequality. Express the solution sets in interval notation. $2 x + 7 < - 1 \text { or } 2 x + 7 > 1$

A) $( - \infty , - 4 ] \cup [ - 3 , \infty )$
B) $( - \infty , \infty )$
C) $( - \infty , - 3 ) \cup ( - 4 , \infty )$
D) $( - \infty , - 4 ) \cup ( - 3 , \infty )$
E) $( - \infty , - 3 ] \cup [ - 4 , \infty )$

Question 42

The ratio of male students to female students at a certain university is 5 to 7. If there is a total of 16,800 students, find the number of male and the number of female students. The number of male students is __________. The number of female students is __________. Please enter your answer as two numbers, separated by a semicolon.

Question 43

Domenica and Javier start from the same location at the same time and ride their bicycles in opposite directions for 4 hours, at which time they are 116 miles apart. Domenica rides 3 miles per hour faster than Javier. Find the rate of each rider. __________ miles per hour for Javier. __________ miles per hour for Domenica. Please enter your answer as two numbers, separated by a comma.

Question 44

The notation $( - \infty , 3 ]$ refers to the interval of all real numbers greater than 3.

Question 45

Multiplying both sides of an inequality by a negative number reverses the inequality symbol.

Question 46

A parenthesis on a graph indicates that the endpoint is to be included in the solution.

Question 47

There are 54 students in a certain class. The number of females is 6 less than three times the number of males. Find the number of females and the number of males in the class. The number of males is __________. The number of females is __________. Please enter your answer as two numbers, separated by a comma.

Question 48

Sean bought 5 lemons and 2 limes for $2.05. At the same prices, Kim bought 4 lemons and 7 limes for $2.45. Find the price per lemon and the price per lime. The price per lemon is $__________. The price per lime is $__________. Please enter your answer as two numbers, separated by a comma.

Question 49

One leg of a right triangle is 7 meters longer than the other leg. If the length of the hypotenuse is 13 meters, find the length of each leg. The length of shorter leg is __________ meters. The length of longer leg is __________ meters. Please enter your answer as two numbers, separated by a comma.

Question 50

Solve the inequality and express the solution set using interval notation. $10 ( x + 2 ) - 5 ( x - 7 ) < 0$

A) $( - 11 , + \infty )$
B) $( - \infty , - 11 )$
C) $( - \infty , - 11 ]$
D) $[ - 11 , + \infty )$

Question 51

Solve the inequality and express the solution set using interval notation. $- 6 ( 6 x + 5 ) - 5 ( 7 x + 4 ) \geq 0$

A) $\left( - \infty , - \frac { 50 } { 71 } \right)$
B) $\left( - \frac { 50 } { 71 } , + \infty \right)$
C) $\left( - \infty , - \frac { 50 } { 71 } \right]$
D) $\left( - \frac { 50 } { 71 } , + \infty \right]$

Question 52

Desa invested a certain amount of money at 4% interest and $2,500 more than that amount at 7%. Her total yearly interest was $725. How much did she invest at each rate? She invested $__________ at 4%. She invested $__________ at 7%. Please enter your answer as two numbers, separated by a semicolon.

Question 53

Solve the inequality and express the solution sets in interval notation. $\frac { x + 3 } { 16 } - \frac { x + 9 } { 9 } \geq \frac { 7 } { 18 }$

A) $\left[ \frac { - 173 } { 7 } , \infty \right)$
B) $\left( - \infty , \frac { - 173 } { 7 } \right)$
C) $\left( - \infty , \frac { - 173 } { 7 } \right]$
D) $( - \infty , 0 ]$
E) $\left( \frac { - 173 } { 7 } , \frac { - 173 } { 7 } \right)$

Question 54

Compound statements that use "or" are called disjunctions.

Question 55

The sum of the present ages of Eric and his father is 56 years. In 8 years, his father will be twice as old as Eric will be at that time. Find their present ages. Eric is __________ years old. His father is __________ years old. Please enter your answer as two numbers, separated by a comma.

Question 56

Solve the inequality and express the solution set using interval notation. $6 ( x - 9 ) - 4 ( x - 12 ) < 20$

A) $( 13 , + \infty )$
B) $( - \infty , 13 ]$
C) $[ 13 , + \infty )$
D) $( - \infty , 13 )$

Question 57

Solve the inequality and express the solution sets in interval notation. $0.08 x + 0.05 ( 5 x ) \geq 33$

A) $( 100 , \infty )$
B) $( - \infty , 100 )$
C) $[ 100 , \infty )$
D) $( - \infty , 100 ]$
E) $[ - 100,100 ]$

Question 58

Solve the inequality and express the solution set using interval notation. $4 ( x - 6 ) \leq - 8 ( x + 6 )$

A) $( - \infty , - 2 )$
B) $( - 2 , + \infty )$
C) $( - \infty , - 2 ]$
D) $[ - 2 , + \infty )$

Question 59

Solve the inequality and express the solution set using interval notation. $- ( x - 2 ) + 4 ( x - 4 ) < 22 ( x + 3 )$

A) $\left[ - \frac { 80 } { 19 } , + \infty \right)$
B) $\left( - \infty , - \frac { 80 } { 19 } \right]$
C) $\left( - \infty , - \frac { 80 } { 19 } \right)$
D) $\left( - \frac { 80 } { 19 } , + \infty \right)$

Question 60

Solve the inequality and express the solution set using interval notation. $0.1 x + 0.05 ( x + 400 ) > 38$

A) $( - \infty , 120 )$
B) $( 120 , \infty )$
C) $( - \infty , 120 ]$
D) $[ 120 , \infty )$
E) $[ 120 , \infty ]$

Question 61

Solve the compound inequality using the compact form. Express the solution sets in interval notation. $- 2 < 1 - x < 2$

A) $( - 3,1 )$
B) $( - 1,3 )$
C) $( - \infty , - 1 )$
D) $( - \infty , 3 )$
E) $( - 1 , \infty )$

Question 62

Solve the inequality and express the solution set using interval notation.

Question 63

Solve the inequality and express the solution set using interval notation.

Question 64

Solve the inequality and express the solution set using interval notation.

Question 65

Solve the inequality and express the solution set using interval notation.

Question 66

Solve the compound inequality and graph the solution sets. $3 x + 2 < - 1 \text { or } 3 x + 2 > 1$

A)
B)
C)
D)
E)

Question 67

The temperatures for a 24-hour period ranged between 13 o F and 5 o F, inclusive. What was the range in Celsius degrees? ( Use ). Please enter your answer in interval notation.

Question 68

Solve the inequality and express the solution set using interval notation. $\frac { x - 4 } { 4 } - \frac { x - 5 } { 6 } \leq \frac { 5 } { 12 }$

A) $( - \infty , 7 ]$
B) $[ - 4 , \infty )$
C) $[ - 7 , \infty )$
D) $( - \infty , 4 ]$
E) $( - \infty , 7 )$

Question 69

Solve the inequality and express the solution sets in interval notation.

Question 70

Solve the compound inequality using the compact form. Express the solution sets in interval notation. $- 4 < 5 x - 3 < 4$

A) $\left( - \infty , - \frac { 1 } { 5 } \right)$
B) $\left( \frac { 1 } { 5 } , \frac { 7 } { 5 } \right)$
C) $\left( - \frac { 1 } { 5 } , \infty \right)$
D) $\left( - \frac { 1 } { 5 } , \frac { 7 } { 5 } \right)$
E) $\left( - \infty , \frac { 7 } { 5 } \right)$

Question 71

Solve the following compound inequality using the compact form. Express the solution sets in interval notation.

Question 72

Candace had scores of 96, 83, 93, and 86 on her first four exams of the semester. What score must she obtain on the fifth exam to have an average of 89.4 or better for the five exams? Please enter your answer as an inequality. Use " x " for decision variable.

Question 73

Marsha bowled 132 and 177 in her first two games. What must she bowl in the third game to have an average of at least 164 for the three games? Please enter your answer as an inequality. Use " x " for decision variable.

Question 74

Solve the compound inequality and graph the solution sets. $2 x - 1 \geq 5 \text { and } x > 0$

A)
B)
C)
D)
E)

Question 75

Solve the inequality and express the solution set using interval notation.

Question 76

Solve the compound inequality. Express the solution sets in interval notation.

Question 77

Solve the inequality and express the solution set using interval notation.

Question 78

A person s intelligence quotient ( I ) is found by dividing mental age ( M ), as indicated by standard tests, by chronological age ( C ) and then multiplying this ratio by 100. The formula can be used. If the I range of a group of 16-year-olds is given by , find the range of the mental age of this group. Please enter your answer in interval notation.

Question 79

A person s intelligence quotient ( I ) is found by dividing mental age ( M ), as indicated by standard tests, by chronological age ( C ) and then multiplying this ratio by 20. The formula $I = \frac { 20 \mathrm { M } } { C }$ can be used. If the I range of a group of 12-year-olds is given by $76 \leq I \leq 189$ , find the range of the mental age of this group.

A) $3.8 \leq M \leq 9.45$
B) $912 \leq M \leq 2268$
C) $76 \leq M \leq 189$
D) $45.6 \leq M \leq 113.4$
E) $91.2 \leq M \leq 226.8$

Question 80

Solve the inequality and express the solution set using interval notation. $x \geq 3.25 + 0.35 x$

A) $( - \infty , 5 ]$
B) $( - \infty , 3 ]$
C) $[ - 5 , \infty )$
D) $[ 3 , \infty )$
E) $[ 5 , \infty )$