Question 1

Solve the equation.
-$$| 8 x - 3 | + 6 = - 3$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ - \frac { 3 } { 2 } , - \frac { 3 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ \frac { 3 } { 2 } , \frac { 3 } { 4 } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ - \frac { 3 } { 2 } , - \frac { 3 } { 4 } \right\}$ 
C)  $\left\{ - \frac { 3 } { 4 } \right\}$ 
D)  $\left\{ \frac { 3 } { 2 } , \frac { 3 } { 4 } \right\}$

Question 2

Solve for y.
-$$4 x ^ { 2 } - y + 6 x = 0$$

Accepted Answer

A)  $y = 4 x ^ { 2 } - 6 x$ 
B)  $y = 4 x ^ { 2 } + 6 x$ 
C)  $y = - 4 x ^ { 2 } + 6 x$ 
D)  $y = - 4 x ^ { 2 } - 6 x$ 
A)  $y = 4 x ^ { 2 } - 6 x$ 
B)  $y = 4 x ^ { 2 } + 6 x$ 
C)  $y = - 4 x ^ { 2 } + 6 x$ 
D)  $y = - 4 x ^ { 2 } - 6 x$

Question 3

Find the quotient. Write the answer in standard form.
-$$\frac { 9 + 2 i } { 4 + 9 i }$$

Accepted Answer

A)  $\frac { 18 } { 97 } - \frac { 89 } { 97 } \mathrm { i }$ 
B)  $\frac { 54 } { 97 } - \frac { 73 } { 97 } \mathrm { i }$ 
C)  $- \frac { 18 } { 65 } - \frac { 73 } { 65 } \mathrm { i }$ 
D)  $- \frac { 54 } { 65 } - \frac { 73 } { 65 } \mathrm { i }$ 
A)  $\frac { 18 } { 97 } - \frac { 89 } { 97 } \mathrm { i }$ 
B)  $\frac { 54 } { 97 } - \frac { 73 } { 97 } \mathrm { i }$ 
C)  $- \frac { 18 } { 65 } - \frac { 73 } { 65 } \mathrm { i }$ 
D)  $- \frac { 54 } { 65 } - \frac { 73 } { 65 } \mathrm { i }$

Question 4

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$0.5 ( x - 3 ) - 0.2 ( x - 3 ) = 0.3 x - 0.9$$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 0.7 \}$ 
C)  Identity; { all real numbers } 
D)  Conditional; $\{ - 3 \}$ 
A)  Contradiction; $\varnothing$ 
B)  Conditional; $\{ 0.7 \}$ 
C)  Identity; { all real numbers } 
D)  Conditional; $\{ - 3 \}$

Question 5

Write the number as the product of a real number and i.
-$\sqrt { - 76 }$

Accepted Answer

A)  $- 2 \sqrt { 19 i }$ 
B)  $2 \sqrt { 19 \mathrm { i } }$ 
C)  $- 2 \mathrm { i } \sqrt { 19 }$ 
D)  $2 \mathrm { i } \sqrt { 19 }$ 
A)  $- 2 \sqrt { 19 i }$ 
B)  $2 \sqrt { 19 \mathrm { i } }$ 
C)  $- 2 \mathrm { i } \sqrt { 19 }$ 
D)  $2 \mathrm { i } \sqrt { 19 }$

Question 6

Solve the equation.
-$$| 7 x - 8 | = | 2 x - 9 |$$

Accepted Answer

A)  $\left\{ - \frac { 17 } { 5 } , 1 \right\}$ 
B)  $\left\{ - \frac { 1 } { 5 } , \frac { 17 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 9 } , \frac { 17 } { 5 } \right\}$ 
D)  $\left\{ \frac { 17 } { 5 } , 1 \right\}$ 
A)  $\left\{ - \frac { 17 } { 5 } , 1 \right\}$ 
B)  $\left\{ - \frac { 1 } { 5 } , \frac { 17 } { 9 } \right\}$ 
C)  $\left\{ - \frac { 1 } { 9 } , \frac { 17 } { 5 } \right\}$ 
D)  $\left\{ \frac { 17 } { 5 } , 1 \right\}$

Question 7

Solve the problem.
-Helen Weller invested $13,000 in an account that pays 1.25% simple interest. How much additional money must be invested in an account that pays 3.5% simple interest so that the average return on
The two investments amounts to 2%?

Accepted Answer

A)  $9000 
B)  $6500 
C)  $13,000 
D)  $10,000 
A)  $9000 
B)  $6500 
C)  $13,000 
D)  $10,000

Question 8

Solve the equation.
-$$x ^ { 2 } + 15 = 0$$

Accepted Answer

A)  $\pm i \sqrt { 15 }$ 
B)  $\pm 15 \mathrm { i }$ 
C)  $\pm 15$ 
D)  $\pm \sqrt { 15 }$ 
A)  $\pm i \sqrt { 15 }$ 
B)  $\pm 15 \mathrm { i }$ 
C)  $\pm 15$ 
D)  $\pm \sqrt { 15 }$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$| - 5 x - 3 | > - 5$$

Accepted Answer

A)  $\left( - \infty , \frac { 2 } { 5 } \right)$ 
B)  $\varnothing$ 
C)  $\left( - \frac { 8 } { 5 } , \frac { 2 } { 5 } \right)$ 
D)  $( - \infty , \infty )$ 
A)  $\left( - \infty , \frac { 2 } { 5 } \right)$ 
B)  $\varnothing$ 
C)  $\left( - \frac { 8 } { 5 } , \frac { 2 } { 5 } \right)$ 
D)  $( - \infty , \infty )$

Question 10

Solve the equation by completing the square.
-$$x ^ { 2 } + 10 x + 16 = 0$$

Accepted Answer

A)  $\{ 24 , - 8 \}$ 
B)  $\{ \pm 4 \}$ 
C)  $\{ - 2 , - 8 \}$ 
D)  $\{ 2,8 \}$ 
A)  $\{ 24 , - 8 \}$ 
B)  $\{ \pm 4 \}$ 
C)  $\{ - 2 , - 8 \}$ 
D)  $\{ 2,8 \}$

Question 11

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt [ 5 ] { 2 x + 3 } = 5$$

Accepted Answer

A)  $\{ 1561 \}$ 
B)  $\{ 3125 \}$ 
C)  $\left\{ \frac { 3125 } { 2 } \right\}$ 
D)  $\{ 3122 \}$ 
A)  $\{ 1561 \}$ 
B)  $\{ 3125 \}$ 
C)  $\left\{ \frac { 3125 } { 2 } \right\}$ 
D)  $\{ 3122 \}$

Question 12

Write the inequality in interval notation.
-

Accepted Answer

A)  $[ 3 , \infty )$ 
B)  $( - \infty , - 2 ]$ 
C)  $[ - 2 , \infty )$ 
D)  $( - \infty , 3 ]$ 
A)  $[ 3 , \infty )$ 
B)  $( - \infty , - 2 ]$ 
C)  $[ - 2 , \infty )$ 
D)  $( - \infty , 3 ]$

Question 13

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$3 ( 12 x + 8 ) = 6 ( 4 x + 22 )$$

Accepted Answer

A)  Contradiction; $\varnothing$ 
B)  Identity; {all real numbers } 
C)  Conditional; $\{ 9 \}$ 
D)  Conditional; $\{ - 13 \}$ 
A)  Contradiction; $\varnothing$ 
B)  Identity; {all real numbers } 
C)  Conditional; $\{ 9 \}$ 
D)  Conditional; $\{ - 13 \}$

Question 14

Solve the inequality. Write the solution set in interval notation.
-$$| 2 x + 2 | < 16$$

Accepted Answer

A)  $( - 9,7 )$ 
B)  $( - \infty , 2 )$ 
C)  $( - \infty , - 9 ) \cup ( 7 , \infty )$ 
D)  $( - \infty , - 9 )$ 
A)  $( - 9,7 )$ 
B)  $( - \infty , 2 )$ 
C)  $( - \infty , - 9 ) \cup ( 7 , \infty )$ 
D)  $( - \infty , - 9 )$

Question 15

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

Accepted Answer

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

Question 16

Indicate whether the statement is true always, sometimes, or never.
-A real number is a complex number.

Accepted Answer

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

Question 17

Find the sum or difference. Write the answer in standard form.
-$$( - 6 - 8 i ) + ( 7 + 3 i ) - 5 i$$

Accepted Answer

A)  $1 + 10 \mathrm { i }$ 
B)  $- 13 - 5 i$ 
C)  $- 4 - 10 \mathrm { i }$ 
D)  $1 - 10 \mathrm { i }$ 
A)  $1 + 10 \mathrm { i }$ 
B)  $- 13 - 5 i$ 
C)  $- 4 - 10 \mathrm { i }$ 
D)  $1 - 10 \mathrm { i }$

Question 18

Simplify the power of i.
-$\frac { 1 } { \mathrm { i } ^ { 45 } }$

Accepted Answer

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

Question 19

Solve for the indicated variable.
-$\frac { 1 } { A } = \frac { 1 } { B } + \frac { 1 } { C }$, for $A$

Accepted Answer

A)  $A = 4 + B + C$ 
B)  $A = \frac { B } { B + C }$ 
C)  $\mathrm { A } = \frac { \mathrm { B } - \mathrm { C } } { \mathrm { BC } }$ 
D)  $A = \frac { B C } { B + C }$ 
A)  $A = 4 + B + C$ 
B)  $A = \frac { B } { B + C }$ 
C)  $\mathrm { A } = \frac { \mathrm { B } - \mathrm { C } } { \mathrm { BC } }$ 
D)  $A = \frac { B C } { B + C }$

Question 20

Decide what values of the variable cannot possibly be solutions for the equation.
-Frank can type a report in 7 hours. James takes 2 hours to type it. How long will it take the two of 312) them typing together?

Accepted Answer

A)  $\frac { 14 } { 5 } \mathrm { hr }$ 
B)  $\frac { 1 } { 9 } \mathrm { hr }$ 
C)  $\frac { 1 } { 14 } \mathrm { hr }$ 
D)  $\frac { 14 } { 9 } \mathrm { hr }$ 
A)  $\frac { 14 } { 5 } \mathrm { hr }$ 
B)  $\frac { 1 } { 9 } \mathrm { hr }$ 
C)  $\frac { 1 } { 14 } \mathrm { hr }$ 
D)  $\frac { 14 } { 9 } \mathrm { hr }$

Solve the equation. - $| 8 x - 3 | + 6 = - 3$

Solve for y. - $4 x ^ { 2 } - y + 6 x = 0$

Find the quotient. Write the answer in standard form. - $\frac { 9 + 2 i } { 4 + 9 i }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $0.5 ( x - 3 ) - 0.2 ( x - 3 ) = 0.3 x - 0.9$

Write the number as the product of a real number and i. - $\sqrt { - 76 }$

Solve the equation. - $| 7 x - 8 | = | 2 x - 9 |$

Solve the problem. -Helen Weller invested $13,000 in an account that pays 1.25% simple interest. How much additional money must be invested in an account that pays 3.5% simple interest so that the average return on The two investments amounts to 2%?

Solve the equation. - $x ^ { 2 } + 15 = 0$

Solve the inequality. Write the solution set in interval notation. - $| - 5 x - 3 | > - 5$

Solve the equation by completing the square. - $x ^ { 2 } + 10 x + 16 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt [ 5 ] { 2 x + 3 } = 5$

Write the inequality in interval notation. -

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $3 ( 12 x + 8 ) = 6 ( 4 x + 22 )$

Solve the inequality. Write the solution set in interval notation. - $| 2 x + 2 | < 16$

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

Indicate whether the statement is true always, sometimes, or never. -A real number is a complex number.

Find the sum or difference. Write the answer in standard form. - $( - 6 - 8 i ) + ( 7 + 3 i ) - 5 i$

Simplify the power of i. - $\frac { 1 } { \mathrm { i } ^ { 45 } }$

Solve for the indicated variable. - $\frac { 1 } { A } = \frac { 1 } { B } + \frac { 1 } { C }$ , for $A$

Decide what values of the variable cannot possibly be solutions for the equation. -Frank can type a report in 7 hours. James takes 2 hours to type it. How long will it take the two of 312) them typing together?

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. - ∣8x−3∣+6=−3| 8 x - 3 | + 6 = - 3∣8x−3∣+6=−3

Solve for y. - 4x2−y+6x=04 x ^ { 2 } - y + 6 x = 04x2−y+6x=0

Find the quotient. Write the answer in standard form. - 9+2i4+9i\frac { 9 + 2 i } { 4 + 9 i }4+9i9+2i​

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - 0.5(x−3)−0.2(x−3)=0.3x−0.90.5 ( x - 3 ) - 0.2 ( x - 3 ) = 0.3 x - 0.90.5(x−3)−0.2(x−3)=0.3x−0.9

Write the number as the product of a real number and i. - −76\sqrt { - 76 }−76​

Solve the equation. - ∣7x−8∣=∣2x−9∣| 7 x - 8 | = | 2 x - 9 |∣7x−8∣=∣2x−9∣