Question 1

Solve the equation.
-$| - 2 + 5 x | = | 7 - 10 x |$

Accepted Answer

A)  $\left\{ - \frac { 9 } { 5 } , - \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } , 1 \right\}$ 
C)  $\left\{ - \frac { 1 } { 3 } , 1 \right\}$ 
D)  $\left\{ \frac { 1 } { 3 } , 1 \right\}$ 
A)  $\left\{ - \frac { 9 } { 5 } , - \frac { 1 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 5 } , 1 \right\}$ 
C)  $\left\{ - \frac { 1 } { 3 } , 1 \right\}$ 
D)  $\left\{ \frac { 1 } { 3 } , 1 \right\}$

Question 2

Solve the equation by the zero-factor property.
-$$x ^ { 2 } + 8 x - 20 = 0$$

Accepted Answer

A)  $\{ 2,10 \}$ 
B)  $\{ - 10 , - 2 \}$ 
C)  $\{ - 2,10 \}$ 
D)  $\{ - 10,2 \}$ 
A)  $\{ 2,10 \}$ 
B)  $\{ - 10 , - 2 \}$ 
C)  $\{ - 2,10 \}$ 
D)  $\{ - 10,2 \}$

Question 3

Solve and graph the inequality. Give answer in interval notation.
-$$- 10 + 8 x + 12 \geq 7 x - 7$$

Accepted Answer

A)  $( - \infty , - 9 ]$
  
B)  $( - \infty , 8 )$
  
C)  $[ - 9 , \infty )$
  
D)  $( 8 , \infty )$
  
A)  $( - \infty , - 9 ]$
  
B)  $( - \infty , 8 )$
  
C)  $[ - 9 , \infty )$
  
D)  $( 8 , \infty )$

Question 4

Write the number in standard form a + bi.
-$$\frac { - 4 + \sqrt { - 80 } } { 32 }$$

Accepted Answer

A)  $- \frac { 1 } { 8 } + \frac { 5 \sqrt { 4 } } { 8 } \mathrm { i }$ 
B)  $- \frac { 1 } { 8 } + \frac { \sqrt { 5 } } { 8 } \mathrm { i }$ 
C)  $- \frac { 1 } { 8 } + \frac { 4 \sqrt { 5 } } { 8 } \mathrm { i }$ 
D)  $- \frac { 1 } { 8 } + \frac { \sqrt { 5 } } { 32 } \mathrm { i }$ 
A)  $- \frac { 1 } { 8 } + \frac { 5 \sqrt { 4 } } { 8 } \mathrm { i }$ 
B)  $- \frac { 1 } { 8 } + \frac { \sqrt { 5 } } { 8 } \mathrm { i }$ 
C)  $- \frac { 1 } { 8 } + \frac { 4 \sqrt { 5 } } { 8 } \mathrm { i }$ 
D)  $- \frac { 1 } { 8 } + \frac { \sqrt { 5 } } { 32 } \mathrm { i }$

Question 5

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$$- 2 , - 8$$

Accepted Answer

A)  $x ^ { 2 } + 10 x + 16 = 0$ 
B)  $x ^ { 2 } + 16 x - 10 = 0$ 
C)  $x ^ { 2 } - 10 x + 16 = 0$ 
D)  $x ^ { 2 } + 16 x + 10 = 0$ 
A)  $x ^ { 2 } + 10 x + 16 = 0$ 
B)  $x ^ { 2 } + 16 x - 10 = 0$ 
C)  $x ^ { 2 } - 10 x + 16 = 0$ 
D)  $x ^ { 2 } + 16 x + 10 = 0$

Question 6

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { x + 9 } { x + 8 } < 6$$

Accepted Answer

A)  $\varnothing$ 
B)  $( - \infty , - 8 ) \cup \left( - \frac { 39 } { 5 } , \infty \right)$ 
C)  $\left( - 8 , - \frac { 39 } { 5 } \right)$ 
D)  $\left( - \infty , - \frac { 39 } { 5 } \right) \cup ( 8 , \infty )$ 
A)  $\varnothing$ 
B)  $( - \infty , - 8 ) \cup \left( - \frac { 39 } { 5 } , \infty \right)$ 
C)  $\left( - 8 , - \frac { 39 } { 5 } \right)$ 
D)  $\left( - \infty , - \frac { 39 } { 5 } \right) \cup ( 8 , \infty )$

Question 7

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( x + 3 ) ^ { 4 } - 5 ( x + 3 ) ^ { 2 } + 4 = 0$$

Accepted Answer

A)  $\{ 1,4 \}$ 
B)  $\{ - 1 , - 4 \}$ 
C)  $\{ - 2 , - 1,1,2 \}$ 
D)  $\{ - 5 , - 4 , - 2 , - 1 \}$ 
A)  $\{ 1,4 \}$ 
B)  $\{ - 1 , - 4 \}$ 
C)  $\{ - 2 , - 1,1,2 \}$ 
D)  $\{ - 5 , - 4 , - 2 , - 1 \}$

Question 8

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 1$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
B)  $\{ 5 \}$ 
C)  $\{ 0 \}$ 
D)  $\varnothing$ 
A)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
B)  $\{ 5 \}$ 
C)  $\{ 0 \}$ 
D)  $\varnothing$

Question 9

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-8,6

Accepted Answer

A)  $x ^ { 2 } + 48 x - 14 = 0$ 
B)  $x ^ { 2 } - 14 x + 48 = 0$ 
C)  $x ^ { 2 } + 14 x + 48 = 0$ 
D)  $x ^ { 2 } + 48 x + 14 = 0$ 
A)  $x ^ { 2 } + 48 x - 14 = 0$ 
B)  $x ^ { 2 } - 14 x + 48 = 0$ 
C)  $x ^ { 2 } + 14 x + 48 = 0$ 
D)  $x ^ { 2 } + 48 x + 14 = 0$

Question 10

Solve the problem.
-A boat is 180 feet from the base of cliff. If the distance from the top of the cliff to the boat is 45 more than twice the height of the cliff. Find the height of the cliff. Round to the nearest tenth of a foot if
Necessary.

Accepted Answer

A)  100.6 ft 
B)  45 ft 
C)  75 ft 
D)  135 ft 
A)  100.6 ft 
B)  45 ft 
C)  75 ft 
D)  135 ft

Question 11

Solve the formula for the indicated variable.
-$S = 2 \pi r h + 2 \pi r ^ { 2 }$, for $h$

Accepted Answer

A)  $h = 2 \pi ( S - r )$ 
B)  $h = \frac { S - 2 \pi r ^ { 2 } } { 2 \pi r }$ 
C)  $h = \frac { S } { 2 \pi r } - 1$ 
D)  $h = S - r$ 
A)  $h = 2 \pi ( S - r )$ 
B)  $h = \frac { S - 2 \pi r ^ { 2 } } { 2 \pi r }$ 
C)  $h = \frac { S } { 2 \pi r } - 1$ 
D)  $h = S - r$

Question 12

Simplify the power of i.
-$\mathrm { i } ^ { - 26 }$

Accepted Answer

A)  i 
B)  -i 
C)  -1 
D)  1 
A)  i 
B)  -i 
C)  -1 
D)  1

Question 13

Find the sum or difference. Write the answer in standard form.
-$$7 \sqrt { 5 } - ( 5 \sqrt { 5 } + i ) + 3 i - ( - 6 \sqrt { 5 } + 3 i )$$

Accepted Answer

A)  $- 8 - 5 i \sqrt { 5 }$ 
B)  $8 \sqrt { 5 } - \mathrm { i }$ 
C)  $8 - 5 i \sqrt { 5 }$ 
D)  $8 \sqrt { 5 } + \mathrm { i }$ 
A)  $- 8 - 5 i \sqrt { 5 }$ 
B)  $8 \sqrt { 5 } - \mathrm { i }$ 
C)  $8 - 5 i \sqrt { 5 }$ 
D)  $8 \sqrt { 5 } + \mathrm { i }$

Question 14

Write the statement as an absolute value inequality.
-A real estate development consists of home sites that range in width from 53 to 105 feet and in depth from 125 to 187 feet. Using $ x $ as the variable in both cases, write absolute value inequalities that correspond to these ranges.

Accepted Answer

A)  $ |x-79| \leq 26,|x-156| \leq 31 $ 
B)  $ |B-52| \leq 53,|x-62| \leq 125 $ 
C)  $ |B-53| \leq 52,|x-125| \leq 62 $ 
D)  $ |x-26| \leq 79,|x-31| \leq 156 $ 
A)  $ |x-79| \leq 26,|x-156| \leq 31 $ 
B)  $ |B-52| \leq 53,|x-62| \leq 125 $ 
C)  $ |B-53| \leq 52,|x-125| \leq 62 $ 
D)  $ |x-26| \leq 79,|x-31| \leq 156 $

Question 15

Solve the equation.
-$$x + 7 = 0$$

Accepted Answer

A)  $- \mathrm { i } \sqrt { 7 }$ 
B)  $- 7$ 
C)  $i \sqrt { 7 }$ 
D)  7 
A)  $- \mathrm { i } \sqrt { 7 }$ 
B)  $- 7$ 
C)  $i \sqrt { 7 }$ 
D)  7

Question 16

Solve the inequality. Write the solution set in interval notation.
-$$( x + 4 ) ( x + 2 ) ( x - 5 ) > 0$$

Accepted Answer

A)  $( 5 , \infty )$ 
B)  $( - 4 , - 2 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 2 )$ 
D)  $( - \infty , - 4 ) \cup ( - 2,5 )$ 
A)  $( 5 , \infty )$ 
B)  $( - 4 , - 2 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , - 2 )$ 
D)  $( - \infty , - 4 ) \cup ( - 2,5 )$

Question 17

Solve the problem.
-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 6 miles per hour, and Delvis is traveling at a speed of 8 miles per hour. In 5 hours what is the distance
Between them (assuming that they began at the same point and time)?

Accepted Answer

A)  11 mi 
B)  19 mi 
C)  7 mi 
D)  10 mi 
A)  11 mi 
B)  19 mi 
C)  7 mi 
D)  10 mi

Question 18

Decide whether or not the equations are equivalent.
-$$\begin{array} { l } 
x = 2 - 4 x \
3 x = 2
\end{array}$$

Accepted Answer

A)  Not equivalent 
B)  Equivalent 
A)  Not equivalent 
B)  Equivalent

Question 19

Solve the equation using the quadratic formula.
-$$6 x ^ { 2 } + 12 x = - 2$$

Accepted Answer

A)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 3 } \right\}$ 
B)  $\left\{ \frac { - 12 \pm \sqrt { 6 } } { 3 } \right\}$ 
C)  $\left\{ \frac { - 3 \pm \sqrt { 6 } } { 3 } \right\}$ 
D)  $\left\{ \frac { - 3 \pm \sqrt { 6 } } { 12 } \right\}$ 
A)  $\left\{ \frac { - 3 \pm \sqrt { 3 } } { 3 } \right\}$ 
B)  $\left\{ \frac { - 12 \pm \sqrt { 6 } } { 3 } \right\}$ 
C)  $\left\{ \frac { - 3 \pm \sqrt { 6 } } { 3 } \right\}$ 
D)  $\left\{ \frac { - 3 \pm \sqrt { 6 } } { 12 } \right\}$

Question 20

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( 3 x + 1 ) ^ { 1 / 2 } = 3 + ( x - 4 ) ^ { 1 / 2 }$$

Accepted Answer

A)  $\{ - 5 , - 8 \}$ 
B)  $\varnothing$ 
C)  $\{ 5,8 \}$ 
D)  $\{ - 1 \}$ 
A)  $\{ - 5 , - 8 \}$ 
B)  $\varnothing$ 
C)  $\{ 5,8 \}$ 
D)  $\{ - 1 \}$

Solve the equation. - $| - 2 + 5 x | = | 7 - 10 x |$

Solve the equation by the zero-factor property. - $x ^ { 2 } + 8 x - 20 = 0$

Solve and graph the inequality. Give answer in interval notation. - $- 10 + 8 x + 12 \geq 7 x - 7$ $Solve and graph the inequality. Give answer in interval notation. - - 10 + 8 x + 12 \geq 7 x - 7$

Write the number in standard form a + bi. - $\frac { - 4 + \sqrt { - 80 } } { 32 }$

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $- 2 , - 8$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { x + 9 } { x + 8 } < 6$

Decide what values of the variable cannot possibly be solutions for the equation. - $( x + 3 ) ^ { 4 } - 5 ( x + 3 ) ^ { 2 } + 4 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 1$

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. -8,6

Solve the problem. -A boat is 180 feet from the base of cliff. If the distance from the top of the cliff to the boat is 45 more than twice the height of the cliff. Find the height of the cliff. Round to the nearest tenth of a foot if Necessary.

Solve the formula for the indicated variable. - $S = 2 \pi r h + 2 \pi r ^ { 2 }$ , for $h$

Simplify the power of i. - $\mathrm { i } ^ { - 26 }$

Find the sum or difference. Write the answer in standard form. - $7 \sqrt { 5 } - ( 5 \sqrt { 5 } + i ) + 3 i - ( - 6 \sqrt { 5 } + 3 i )$

Write the statement as an absolute value inequality. -A real estate development consists of home sites that range in width from 53 to 105 feet and in depth from 125 to 187 feet. Using $x$ as the variable in both cases, write absolute value inequalities that correspond to these ranges.

Solve the equation. - $x + 7 = 0$

Solve the inequality. Write the solution set in interval notation. - $( x + 4 ) ( x + 2 ) ( x - 5 ) > 0$

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 6 miles per hour, and Delvis is traveling at a speed of 8 miles per hour. In 5 hours what is the distance Between them (assuming that they began at the same point and time)?

Decide whether or not the equations are equivalent. - x=2-4x 3x=2

Solve the equation using the quadratic formula. - $6 x ^ { 2 } + 12 x = - 2$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 3 x + 1 ) ^ { 1 / 2 } = 3 + ( x - 4 ) ^ { 1 / 2 }$

Review of Basic Concepts

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 2: Equations and Inequalities

Solve the equation. - ∣−2+5x∣=∣7−10x∣| - 2 + 5 x | = | 7 - 10 x |∣−2+5x∣=∣7−10x∣

Solve the equation by the zero-factor property. - x2+8x−20=0x ^ { 2 } + 8 x - 20 = 0x2+8x−20=0

Solve and graph the inequality. Give answer in interval notation. - −10+8x+12≥7x−7- 10 + 8 x + 12 \geq 7 x - 7−10+8x+12≥7x−7

Write the number in standard form a + bi. - −4+−8032\frac { - 4 + \sqrt { - 80 } } { 32 }32−4+−80​​

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - −2,−8- 2 , - 8−2,−8

Solve the rational inequality. Write the solution set in interval notation. - x+9x+8<6\frac { x + 9 } { x + 8 } < 6x+8x+9​<6

Decide what values of the variable cannot possibly be solutions for the equation. - (x+3)4−5(x+3)2+4=0( x + 3 ) ^ { 4 } - 5 ( x + 3 ) ^ { 2 } + 4 = 0(x+3)4−5(x+3)2+4=0

Decide what values of the variable cannot possibly be solutions for the equation. - 3x−2+11+x=−1\sqrt { 3 x - 2 } + \sqrt { 11 + x } = - 13x−2​+11+x​=−1