Question 1

Solve the equation by the square root property.
-$$( x + 9 ) ^ { 2 } = - 6$$

Accepted Answer

A)  $\{ - 9 \pm \sqrt { 6 } \}$ 
B)  $\{ - 9 \pm i \sqrt { 6 } \}$ 
C)  $\{ - 3 - \sqrt { 6 } \}$ 
D)  $\{ - 3,15 \}$ 
A)  $\{ - 9 \pm \sqrt { 6 } \}$ 
B)  $\{ - 9 \pm i \sqrt { 6 } \}$ 
C)  $\{ - 3 - \sqrt { 6 } \}$ 
D)  $\{ - 3,15 \}$ B

Question 2

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 0$$

Accepted Answer

A)  $\left\{ - \frac { 14 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 14 } \right\}$ 
C)  $\left\{ \frac { 14 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 14 } \right\}$ 
A)  $\left\{ - \frac { 14 } { 3 } \right\}$ 
B)  $\left\{ \frac { 3 } { 14 } \right\}$ 
C)  $\left\{ \frac { 14 } { 3 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 14 } \right\}$ D

Question 3

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 1 } { x - 3 } - \frac { 1 } { x + 7 } = 12$$

Accepted Answer

A)  $- 7,3$ 
B)  $- \frac { 1 } { 7 } , \frac { 1 } { 3 }$ 
C)  $- 3,7$ 
D)  $- \frac { 1 } { 3 } , \frac { 1 } { 7 }$ 
A)  $- 7,3$ 
B)  $- \frac { 1 } { 7 } , \frac { 1 } { 3 }$ 
C)  $- 3,7$ 
D)  $- \frac { 1 } { 3 } , \frac { 1 } { 7 }$ A

Question 4

Solve the equation.
-$$| 9 x - 2 | = 3$$

Accepted Answer

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

Question 5

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt [ 3 ] { 4 x + 4 } = - 3$$

Accepted Answer

A)  $\left\{ \frac { 23 } { 4 } \right\}$ 
B)  $\left\{ \frac { 31 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 31 } { 4 } \right\}$ 
D)  $\{ - 31 \}$ 
A)  $\left\{ \frac { 23 } { 4 } \right\}$ 
B)  $\left\{ \frac { 31 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 31 } { 4 } \right\}$ 
D)  $\{ - 31 \}$

Question 6

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

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 0 , - 3 \}$ 
C)  $\{ 0 \}$ 
D)  $\{ 0,9 \}$ 
A)  $\varnothing$ 
B)  $\{ 0 , - 3 \}$ 
C)  $\{ 0 \}$ 
D)  $\{ 0,9 \}$

Question 7

Solve the equation by the square root property.
-$$( 9 x - 9 ) ^ { 2 } = 3$$

Accepted Answer

A)  $\left\{ \pm \frac { \sqrt { 3 } } { 9 } \mathrm { i } \right\}$ 
B)  $\{ 9 \pm \sqrt { 3 } \}$ 
C)  $\left\{ \frac { 9 + \sqrt { 3 } } { 9 } \right\}$ 
D)  $\left\{ \frac { 9 \pm \sqrt { 3 } } { 9 } \right\}$ 
A)  $\left\{ \pm \frac { \sqrt { 3 } } { 9 } \mathrm { i } \right\}$ 
B)  $\{ 9 \pm \sqrt { 3 } \}$ 
C)  $\left\{ \frac { 9 + \sqrt { 3 } } { 9 } \right\}$ 
D)  $\left\{ \frac { 9 \pm \sqrt { 3 } } { 9 } \right\}$

Question 8

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$8 ( x - 7 ) + ( - 16 x ) = - 8 ( x + 4 ) + 16$$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 1 \}$ 
C)  Identity; {all real numbers } 
D)  Conditional; $\{ 0 \}$ 
A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 1 \}$ 
C)  Identity; {all real numbers } 
D)  Conditional; $\{ 0 \}$

Question 9

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }$$

Accepted Answer

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

Question 10

Write the statement as an absolute value inequality.
-The high temperature on December 12 in Biloxi, MS ranges from $ 31^{\circ} \mathrm{F} $ to $ 89^{\circ} \mathrm{F} $. Using $ \mathrm{F} $ as the variable, write an absolute value inequality that corresponds to this range.

Accepted Answer

A)  $ |F-29| \leq 60 $ 
B)  $ |F-60| \leq 29 $ 
C)  $ |F-31| \leq 58 $ 
D)  $ |F-58| \leq 31 $ 
A)  $ |F-29| \leq 60 $ 
B)  $ |F-60| \leq 29 $ 
C)  $ |F-31| \leq 58 $ 
D)  $ |F-58| \leq 31 $

Question 11

Solve and graph the inequality. Give answer in interval notation.
-$$- 15 < 3 x + 3 \leq - 3$$

Accepted Answer

A)  $( - 6 , - 2 )$
  
B)  $[ - 6 , - 2 )$
  
C)  $[ - 6 , - 2 ]$
  
D)  $( - 6 , - 2 ]$
  
A)  $( - 6 , - 2 )$
  
B)  $[ - 6 , - 2 )$
  
C)  $[ - 6 , - 2 ]$
  
D)  $( - 6 , - 2 ]$

Question 12

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { x + 35 } { 10 } = \frac { 5 x - 5 } { x }$$

Accepted Answer

A)  $\left\{ \frac { 50 } { 13 } \right\}$ 
B)  $\{ - 5 , - 10 \}$ 
C)  $\{ 5,10 \}$ 
D)  $\left\{ \frac { 95 } { 49 } \right\}$ 
A)  $\left\{ \frac { 50 } { 13 } \right\}$ 
B)  $\{ - 5 , - 10 \}$ 
C)  $\{ 5,10 \}$ 
D)  $\left\{ \frac { 95 } { 49 } \right\}$

Question 13

Solve the problem.
-A circular hole is filled with concrete to make a footing for a load-bearing pier. The hole measures 18 inches across and requires 2.1 bags of concrete in order to fill it to ground level. What is the
Depth of the hole? Round your answer to the nearest inch. (One bag of concrete, when mixed with
The appropriate amount of water, makes 1800 in.3 of material.)

Accepted Answer

A)  19 in. 
B)  21 in. 
C)  15 in. 
D)  12 in. 
A)  19 in. 
B)  21 in. 
C)  15 in. 
D)  12 in.

Question 14

Solve the equation by the square root property.
-$$x ^ { 2 } = 169$$

Accepted Answer

A)  $\{ \pm 13 \mathrm { i } \}$ 
B)  $\{ 13 \}$ 
C)  $\{ \pm 13 \}$ 
D)  $\{ 84.5 \}$ 
A)  $\{ \pm 13 \mathrm { i } \}$ 
B)  $\{ 13 \}$ 
C)  $\{ \pm 13 \}$ 
D)  $\{ 84.5 \}$

Question 15

Determine whether or not the equation is linear.
-$2 x + 5 ( x - 2 ) = 16 x$

Accepted Answer

A)  Linear 
B)  Not linear 
A)  Linear 
B)  Not linear

Question 16

Solve the inequality. Write the solution set in interval notation.
-$$| 8 x + 1 | - 2 < 0$$

Accepted Answer

A)  $\left( - \infty , - \frac { 3 } { 8 } \right) \cup \left( \frac { 1 } { 8 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 3 } { 8 } \right)$ 
C)  $\varnothing$ 
D)  $\left( - \frac { 3 } { 8 } , \frac { 1 } { 8 } \right)$ 
A)  $\left( - \infty , - \frac { 3 } { 8 } \right) \cup \left( \frac { 1 } { 8 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 3 } { 8 } \right)$ 
C)  $\varnothing$ 
D)  $\left( - \frac { 3 } { 8 } , \frac { 1 } { 8 } \right)$

Question 17

Solve the equation.
-$$| 3 x + 7 | = | x + 5 |$$

Accepted Answer

A)  $\{ - 1 \}$ 
B)  $\{ - 1 , - 3 \}$ 
C)  $\{ 1,3 \}$ 
D)  $\varnothing$ 
A)  $\{ - 1 \}$ 
B)  $\{ - 1 , - 3 \}$ 
C)  $\{ 1,3 \}$ 
D)  $\varnothing$

Question 18

Indicate whether the statement is true always, sometimes, or never.
-$$\text { To find the quotient } \frac { 10 + 3 \mathrm { i } } { 10 - 3 \mathrm { i } } \text {, multiply numerator and denominator by } 10 + 3 \mathrm { i } \text {. }$$

Accepted Answer

A)  Never 
B)  Sometimes 
C)  Always 
A)  Never 
B)  Sometimes 
C)  Always

Question 19

Solve the quadratic inequality. Write the solution set in interval notation.
-$$( x - 4 ) ( x + 3 ) > 0$$

Accepted Answer

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

Question 20

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 3 x - 10 < 0$$

Accepted Answer

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

Solve the equation by the square root property. - $( x + 9 ) ^ { 2 } = - 6$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { x - 3 } - \frac { 1 } { x + 7 } = 12$

Solve the equation. - $| 9 x - 2 | = 3$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 3 ] { 4 x + 4 } = - 3$

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

Solve the equation by the square root property. - $( 9 x - 9 ) ^ { 2 } = 3$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $8 ( x - 7 ) + ( - 16 x ) = - 8 ( x + 4 ) + 16$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }$

Write the statement as an absolute value inequality. -The high temperature on December 12 in Biloxi, MS ranges from $31^{\circ} \mathrm{F}$ to $89^{\circ} \mathrm{F}$ . Using $\mathrm{F}$ as the variable, write an absolute value inequality that corresponds to this range.

Solve and graph the inequality. Give answer in interval notation. - $- 15 < 3 x + 3 \leq - 3$ $Solve and graph the inequality. Give answer in interval notation. - - 15 < 3 x + 3 \leq - 3$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x + 35 } { 10 } = \frac { 5 x - 5 } { x }$

Solve the equation by the square root property. - $x ^ { 2 } = 169$

Determine whether or not the equation is linear. - $2 x + 5 ( x - 2 ) = 16 x$

Solve the inequality. Write the solution set in interval notation. - $| 8 x + 1 | - 2 < 0$

Solve the equation. - $| 3 x + 7 | = | x + 5 |$

Indicate whether the statement is true always, sometimes, or never. - $\text { To find the quotient } \frac { 10 + 3 \mathrm { i } } { 10 - 3 \mathrm { i } } \text {, multiply numerator and denominator by } 10 + 3 \mathrm { i } \text {. }$

Solve the quadratic inequality. Write the solution set in interval notation. - $( x - 4 ) ( x + 3 ) > 0$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 3 x - 10 < 0$

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 by the square root property. - (x+9)2=−6( x + 9 ) ^ { 2 } = - 6(x+9)2=−6

Decide what values of the variable cannot possibly be solutions for the equation. - 4+6x3−1−8x3=0\sqrt [ 3 ] { 4 + 6 x } - \sqrt [ 3 ] { 1 - 8 x } = 034+6x​−31−8x​=0

Decide what values of the variable cannot possibly be solutions for the equation. - 1x−3−1x+7=12\frac { 1 } { x - 3 } - \frac { 1 } { x + 7 } = 12x−31​−x+71​=12

Solve the equation. - ∣9x−2∣=3| 9 x - 2 | = 3∣9x−2∣=3

Decide what values of the variable cannot possibly be solutions for the equation. - 4x+43=−3\sqrt [ 3 ] { 4 x + 4 } = - 334x+4​=−3

Decide what values of the variable cannot possibly be solutions for the equation. - x1/2=−3x1/4x ^ { 1 / 2 } = - 3 x ^ { 1 / 4 }x1/2=−3x1/4

Solve the equation by the square root property. - (9x−9)2=3( 9 x - 9 ) ^ { 2 } = 3(9x−9)2=3

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 8(x−7)+(−16x)=−8(x+4)+168 ( x - 7 ) + ( - 16 x ) = - 8 ( x + 4 ) + 168(x−7)+(−16x)=−8(x+4)+16

Decide what values of the variable cannot possibly be solutions for the equation. - 3x+1=3+x−4\sqrt { 3 x + 1 } = 3 + \sqrt { x - 4 }3x+1​=3+x−4​

Write the statement as an absolute value inequality. -The high temperature on December 12 in Biloxi, MS ranges from 31∘F 31^{\circ} \mathrm{F} 31∘F to 89∘F 89^{\circ} \mathrm{F} 89∘F . Using F \mathrm{F} F as the variable, write an absolute value inequality that corresponds to this range.

Solve and graph the inequality. Give answer in interval notation. - −15<3x+3≤−3- 15 < 3 x + 3 \leq - 3−15<3x+3≤−3

Decide what values of the variable cannot possibly be solutions for the equation. - x+3510=5x−5x\frac { x + 35 } { 10 } = \frac { 5 x - 5 } { x }10x+35​=x5x−5​

Solve the equation by the square root property. - x2=169x ^ { 2 } = 169x2=169

Determine whether or not the equation is linear. - 2x+5(x−2)=16x2 x + 5 ( x - 2 ) = 16 x2x+5(x−2)=16x

Solve the inequality. Write the solution set in interval notation. - ∣8x+1∣−2<0| 8 x + 1 | - 2 < 0∣8x+1∣−2<0

Solve the equation. - ∣3x+7∣=∣x+5∣| 3 x + 7 | = | x + 5 |∣3x+7∣=∣x+5∣

Solve the quadratic inequality. Write the solution set in interval notation. - (x−4)(x+3)>0( x - 4 ) ( x + 3 ) > 0(x−4)(x+3)>0

Solve the quadratic inequality. Write the solution set in interval notation. - x2−3x−10<0x ^ { 2 } - 3 x - 10 < 0x2−3x−10<0