Question 1

Solve the equation.
-$0.5 x - 0.2 ( 30 + x ) = 0.5 ( 30 )$

Accepted Answer

A)  $\{ 60 \}$ 
B)  $\{ 35 \}$ 
C)  $\{ 70 \}$ 
D)  $\{ 80 \}$ 
A)  $\{ 60 \}$ 
B)  $\{ 35 \}$ 
C)  $\{ 70 \}$ 
D)  $\{ 80 \}$ C

Question 2

Solve the equation.
-$0.5 ( 4200 ) + 0.08 \mathrm { p } = 0.6 ( 4200 + \mathrm { p } )$

Accepted Answer

A)  $\{ - 8076.9231 \}$ 
B)  $\{ - 218.4 \}$ 
C)  $\{ - 2184 \}$ 
D)  $\{ - 807.69 \}$ 
A)  $\{ - 8076.9231 \}$ 
B)  $\{ - 218.4 \}$ 
C)  $\{ - 2184 \}$ 
D)  $\{ - 807.69 \}$ D

Question 3

Solve the inequality, giving its solution set in both interval and graph forms.
-$\frac { a } { - 5 } < 4$

Accepted Answer

A)  $[ - 20 , \infty )$
  
B)  $( - \infty , - 20 ]$
  
C)  $( - \infty , - 20 )$
  
D)  $( - 20 , \infty )$
  
A)  $[ - 20 , \infty )$
  
B)  $( - \infty , - 20 ]$
  
C)  $( - \infty , - 20 )$
  
D)  $( - 20 , \infty )$
  D

Question 4

Solve the problem.
-Find the missing length in the similar triangles.

Accepted Answer

A)  x=12 
B)  $x = 11$ 
C)  $x = 4$ 
D)  $x = 16$ 
A)  x=12 
B)  $x = 11$ 
C)  $x = 4$ 
D)  $x = 16$

Question 5

Solve the problem.
-If 3 is subtracted from a number and this difference is doubled, the result is 7 more than the number. Find the number.

Accepted Answer

A) -13 
B) 13 
C) 3 
D) -3 
A) -13 
B) 13 
C) 3 
D) -3

Question 6

Solve the equation.
-$2 [ 3 - 3 ( x + 1 ) ] + 1 = 2 ( - 25 - x ) + 2 x + 25$

Accepted Answer

A)  $\left\{ \frac { 13 } { 3 } \right\}$ 
B)  $\{ 13 \rangle$ 
C)  $\left\{ \frac { 13 } { 6 } \right\}$ 
D)  $\{ 0 \}$ 
A)  $\left\{ \frac { 13 } { 3 } \right\}$ 
B)  $\{ 13 \rangle$ 
C)  $\left\{ \frac { 13 } { 6 } \right\}$ 
D)  $\{ 0 \}$

Question 7

The force required to compress a spring varies directly as the change in the length of the spring. If a force of 18 pounds is required to compress a certain spring 4 inches, how much force is required to
Compress the spring 7 inches?

Accepted Answer

A) 31.5 pounds 
B) 21 pounds 
C) 10.3 pounds 
D) 35 pounds 
A) 31.5 pounds 
B) 21 pounds 
C) 10.3 pounds 
D) 35 pounds

Question 8

Evaluate the expression.
-$4 ^ { - 3 }$

Accepted Answer

A)  $\frac { 1 } { - 64 }$ 
B)  $\frac { 1 } { 64 }$ 
C)  $- 64$ 
D)  64 
A)  $\frac { 1 } { - 64 }$ 
B)  $\frac { 1 } { 64 }$ 
C)  $- 64$ 
D)  64

Question 9

Solve and graph.
-$- 3 ( 5 y + 2 ) < - 18 y - 18$

Accepted Answer

A)  $(-\infty,-4]$
  
B)  $( - 4 , x )$
  
C) $( - \infty , 8 ]$
  
D)  $( - \infty , - 4 )$
  
A)  $(-\infty,-4]$
  
B)  $( - 4 , x )$
  
C) $( - \infty , 8 ]$
  
D)  $( - \infty , - 4 )$

Question 10

The equation is a contradiction.
-Find all values of s that make this statement true: $2 ( 4 s - 7 ) = 8 s - 14$

Accepted Answer

The answer of The equation is a contradiction.
-Find all values...

Question 11

Solve the inequality, then graph the solution.
-$6 \leq \frac{3 x-1}{4} \leq 12$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

Solve the equation.
-$4 - 10 x = - 6$

Accepted Answer

A)  $\left\{ \frac { 2 } { 5 } \right\}$ 
B)  $\{ 1 \}$ 
C)  $\left\{ - \frac { 2 } { 5 } \right\}$ 
D)  $\{ - 1 \}$ 
A)  $\left\{ \frac { 2 } { 5 } \right\}$ 
B)  $\{ 1 \}$ 
C)  $\left\{ - \frac { 2 } { 5 } \right\}$ 
D)  $\{ - 1 \}$

Question 13

How many liters of a 40% alcohol solution must be mixed with 60 liters of a 70% solution to get a 50% solution?

Accepted Answer

A) 180 liters 
B) 12 liters 
C) 18 liters 
D) 120 liters 
A) 180 liters 
B) 12 liters 
C) 18 liters 
D) 120 liters

Question 14

Solve the equation.
-$5 ( y + 4 ) = 6 ( y - 6 )$

Accepted Answer

A)  $\{ - 56 \}$ 
B)  $\{ 56 \}$ 
C)  $\{ 16 \}$ 
D)  $\{ - 16 \}$ 
A)  $\{ - 56 \}$ 
B)  $\{ 56 \}$ 
C)  $\{ 16 \}$ 
D)  $\{ - 16 \}$

Question 15

Evaluate.
-$( - 9 ) ^ { 0 }$

Accepted Answer

A)  $- 1$ 
B)  9 
C)  1 
D)  0 
A)  $- 1$ 
B)  9 
C)  1 
D)  0

Question 16

Paul has grades of 78 and 62 on his first two tests. What must he score on his third test in order to have an average of at least 60?

Accepted Answer

A) at least 40 
B) at most 67 
C) at most 60 
D) at least 70 
A) at least 40 
B) at most 67 
C) at most 60 
D) at least 70

Question 17

If m varies directly as p, and m = 27 when p = 9, find m when p is 8.

Accepted Answer

A) m = 64 
B) m = 81 
C) m = 9 
D) m = 24 
A) m = 64 
B) m = 81 
C) m = 9 
D) m = 24

Question 18

Solve and graph.
-$21 n - 9 \leq 3 ( 6 n - 2 )$

Accepted Answer

A)  $( - \infty , 1 )$
  
B)  $[ 1 , \infty )$
  
C)  $[ - \infty , - 5 )$
  
D)  $( - \infty , 1 ]$
  
A)  $( - \infty , 1 )$
  
B)  $[ 1 , \infty )$
  
C)  $[ - \infty , - 5 )$
  
D)  $( - \infty , 1 ]$

Question 19

Solve the formula for the specified variable.
-$I = \frac { n E } { n r + R } ;$ for $n$

Accepted Answer

A)  $n = \frac { I R } { E - I r }$ 
B)  $n = \operatorname { IR } ( \operatorname { Ir } - \mathrm { E } )$ 
C)  $n = \frac { I R } { I r + E }$ 
D)  $n = \frac { - R } { I r - E }$ 
A)  $n = \frac { I R } { E - I r }$ 
B)  $n = \operatorname { IR } ( \operatorname { Ir } - \mathrm { E } )$ 
C)  $n = \frac { I R } { I r + E }$ 
D)  $n = \frac { - R } { I r - E }$

Question 20

The grading scale for a C in Amy's biology class is an average on tests between 70% and 80%, inclusive. Amy has 64%, 84%, and 78% on the first three tests this semester. What range of scores on
The fourth test would give her a C?

Accepted Answer

A) Between 59% and 89%, inclusive 
B) 89% or better 
C) Between 54% and 94%, inclusive 
D) Between 70% and 80%, inclusive 
A) Between 59% and 89%, inclusive 
B) 89% or better 
C) Between 54% and 94%, inclusive 
D) Between 70% and 80%, inclusive

Solve the equation. - $0.5 x - 0.2 ( 30 + x ) = 0.5 ( 30 )$

Solve the equation. - $0.5 ( 4200 ) + 0.08 \mathrm { p } = 0.6 ( 4200 + \mathrm { p } )$

Solve the inequality, giving its solution set in both interval and graph forms. - $\frac { a } { - 5 } < 4$ $Solve the inequality, giving its solution set in both interval and graph forms. - \frac { a } { - 5 } < 4$

Solve the problem. -Find the missing length in the similar triangles.

Solve the problem. -If 3 is subtracted from a number and this difference is doubled, the result is 7 more than the number. Find the number.

Solve the equation. - $2 [ 3 - 3 ( x + 1 ) ] + 1 = 2 ( - 25 - x ) + 2 x + 25$

The force required to compress a spring varies directly as the change in the length of the spring. If a force of 18 pounds is required to compress a certain spring 4 inches, how much force is required to Compress the spring 7 inches?

Evaluate the expression. - $4 ^ { - 3 }$

Solve and graph. - $- 3 ( 5 y + 2 ) < - 18 y - 18$

The equation is a contradiction. -Find all values of s that make this statement true: $2 ( 4 s - 7 ) = 8 s - 14$

Solve the inequality, then graph the solution. - $6 \leq \frac{3 x-1}{4} \leq 12$

Solve the equation. - $4 - 10 x = - 6$

How many liters of a 40% alcohol solution must be mixed with 60 liters of a 70% solution to get a 50% solution?

Solve the equation. - $5 ( y + 4 ) = 6 ( y - 6 )$

Evaluate. - $( - 9 ) ^ { 0 }$

Paul has grades of 78 and 62 on his first two tests. What must he score on his third test in order to have an average of at least 60?

If m varies directly as p, and m = 27 when p = 9, find m when p is 8.

Solve and graph. - $21 n - 9 \leq 3 ( 6 n - 2 )$ $Solve and graph. - 21 n - 9 \leq 3 ( 6 n - 2 )$

Solve the formula for the specified variable. - $I = \frac { n E } { n r + R } ;$ for $n$

The grading scale for a C in Amy's biology class is an average on tests between 70% and 80%, inclusive. Amy has 64%, 84%, and 78% on the first three tests this semester. What range of scores on The fourth test would give her a C?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 7: The Basic Concepts of Algebra

Solve the equation. - 0.5x−0.2(30+x)=0.5(30)0.5 x - 0.2 ( 30 + x ) = 0.5 ( 30 )0.5x−0.2(30+x)=0.5(30)

Solve the equation. - 0.5(4200)+0.08p=0.6(4200+p)0.5 ( 4200 ) + 0.08 \mathrm { p } = 0.6 ( 4200 + \mathrm { p } )0.5(4200)+0.08p=0.6(4200+p)

Solve the inequality, giving its solution set in both interval and graph forms. - a−5<4\frac { a } { - 5 } < 4−5a​<4

Solve the problem. -Find the missing length in the similar triangles.

Solve the problem. -If 3 is subtracted from a number and this difference is doubled, the result is 7 more than the number. Find the number.

Solve the equation. - 2[3−3(x+1)]+1=2(−25−x)+2x+252 [ 3 - 3 ( x + 1 ) ] + 1 = 2 ( - 25 - x ) + 2 x + 252[3−3(x+1)]+1=2(−25−x)+2x+25

The force required to compress a spring varies directly as the change in the length of the spring. If a force of 18 pounds is required to compress a certain spring 4 inches, how much force is required to Compress the spring 7 inches?

Evaluate the expression. - 4−34 ^ { - 3 }4−3

Solve and graph. - −3(5y+2)<−18y−18- 3 ( 5 y + 2 ) < - 18 y - 18−3(5y+2)<−18y−18

The equation is a contradiction. -Find all values of s that make this statement true: 2(4s−7)=8s−142 ( 4 s - 7 ) = 8 s - 142(4s−7)=8s−14

Solve the inequality, then graph the solution. - 6≤3x−14≤126 \leq \frac{3 x-1}{4} \leq 126≤43x−1​≤12

Solve the equation. - 4−10x=−64 - 10 x = - 64−10x=−6

How many liters of a 40% alcohol solution must be mixed with 60 liters of a 70% solution to get a 50% solution?

Solve the equation. - 5(y+4)=6(y−6)5 ( y + 4 ) = 6 ( y - 6 )5(y+4)=6(y−6)

Evaluate. - (−9)0( - 9 ) ^ { 0 }(−9)0

Paul has grades of 78 and 62 on his first two tests. What must he score on his third test in order to have an average of at least 60?

If m varies directly as p, and m = 27 when p = 9, find m when p is 8.

Solve and graph. - 21n−9≤3(6n−2)21 n - 9 \leq 3 ( 6 n - 2 )21n−9≤3(6n−2)

Solve the formula for the specified variable. - I=nEnr+R;I = \frac { n E } { n r + R } ;I=nr+RnE​; for nnn

The grading scale for a C in Amy's biology class is an average on tests between 70% and 80%, inclusive. Amy has 64%, 84%, and 78% on the first three tests this semester. What range of scores on The fourth test would give her a C?

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Solve the equation. - $0.5 x - 0.2 ( 30 + x ) = 0.5 ( 30 )$

Solve the equation. - $0.5 ( 4200 ) + 0.08 \mathrm { p } = 0.6 ( 4200 + \mathrm { p } )$

Solve the inequality, giving its solution set in both interval and graph forms. - $\frac { a } { - 5 } < 4$ $Solve the inequality, giving its solution set in both interval and graph forms. - \frac { a } { - 5 } < 4$

Solve the equation. - $2 [ 3 - 3 ( x + 1 ) ] + 1 = 2 ( - 25 - x ) + 2 x + 25$

Evaluate the expression. - $4 ^ { - 3 }$

Solve and graph. - $- 3 ( 5 y + 2 ) < - 18 y - 18$

The equation is a contradiction. -Find all values of s that make this statement true: $2 ( 4 s - 7 ) = 8 s - 14$

Solve the inequality, then graph the solution. - $6 \leq \frac{3 x-1}{4} \leq 12$

Solve the equation. - $4 - 10 x = - 6$

Solve the equation. - $5 ( y + 4 ) = 6 ( y - 6 )$

Evaluate. - $( - 9 ) ^ { 0 }$

Solve and graph. - $21 n - 9 \leq 3 ( 6 n - 2 )$ $Solve and graph. - 21 n - 9 \leq 3 ( 6 n - 2 )$

Solve the formula for the specified variable. - $I = \frac { n E } { n r + R } ;$ for $n$