Question 1

Solve for y.
-$$5 x + 8 = 6 y - 9$$

Accepted Answer

A)  $y = \frac { 5 x - 17 } { 6 }$ 
B)  $y = \frac { 5 x + 17 } { 6 }$ 
C)  $y = 5 x + 17$ 
D)  $y = 5 x - 17$ 
A)  $y = \frac { 5 x - 17 } { 6 }$ 
B)  $y = \frac { 5 x + 17 } { 6 }$ 
C)  $y = 5 x + 17$ 
D)  $y = 5 x - 17$

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$\left| \frac { 5 } { 8 } - \frac { 1 } { 9 } x \right| > \frac { 2 } { 11 }$$

Accepted Answer

A)  $\left( - \infty , - \frac { 639 } { 88 } \right) \cup \left( \frac { 351 } { 88 } , \infty \right)$ 
B)  $( - \infty , \infty )$ 
C)  $\left( \frac { 351 } { 88 } , \frac { 639 } { 88 } \right)$ 
D)  $\left( - \infty , \frac { 351 } { 88 } \right) \cup \left( \frac { 639 } { 88 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 639 } { 88 } \right) \cup \left( \frac { 351 } { 88 } , \infty \right)$ 
B)  $( - \infty , \infty )$ 
C)  $\left( \frac { 351 } { 88 } , \frac { 639 } { 88 } \right)$ 
D)  $\left( - \infty , \frac { 351 } { 88 } \right) \cup \left( \frac { 639 } { 88 } , \infty \right)$

Question 3

Solve the equation.
-$$| 7 x + 6 | = | 6 x + 3 |$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 13 } , - 9 \right\}$ 
B)  $\left\{ - 3 , - \frac { 9 } { 13 } \right\}$ 
C)  $\{ - 9,1 \}$ 
D)  $\{ 9,1 \}$ 
A)  $\left\{ - \frac { 3 } { 13 } , - 9 \right\}$ 
B)  $\left\{ - 3 , - \frac { 9 } { 13 } \right\}$ 
C)  $\{ - 9,1 \}$ 
D)  $\{ 9,1 \}$

Question 4

Solve the problem.
-In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 28° greater than that of angle A. Find the measure of the angles.

Accepted Answer

A)  19° , 66° and 95° 
B)  19° , 47° and 133° 
C)  19° , 66° and 114° 
D)  19° , 47° and 114° 
A)  19° , 66° and 95° 
B)  19° , 47° and 133° 
C)  19° , 66° and 114° 
D)  19° , 47° and 114°

Question 5

Find the product. Write the answer in standard form.
-$$( \sqrt { 2 } + 8 i ) ( \sqrt { 2 } - 8 i )$$

Accepted Answer

A)  $2 - 64 i$ 
B)  $2 + 64 \mathrm { i }$ 
C)  $- 6$ 
D)  66 
A)  $2 - 64 i$ 
B)  $2 + 64 \mathrm { i }$ 
C)  $- 6$ 
D)  66

Question 6

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$\sqrt { - 13 }$

Accepted Answer

A)  Complex, pure imaginary, nonreal complex 
B)  Real, complex 
C)  Nonreal complex 
D)  Complex 
A)  Complex, pure imaginary, nonreal complex 
B)  Real, complex 
C)  Nonreal complex 
D)  Complex

Question 7

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\left( x ^ { 2 } + 2 \right) ^ { 1 / 2 } - ( 2 x + 5 ) ^ { 1 / 2 } = 0$$

Accepted Answer

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

Question 8

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 2 } { ( x + 7 ) ^ { 2 } } < 0$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 7 )$ 
C)  $\varnothing$ 
D)  $( - 7,0 )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 7 )$ 
C)  $\varnothing$ 
D)  $( - 7,0 )$

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.
-$$8 + 4 \sqrt { 2 } , 8 - 4 \sqrt { 2 }$$

Accepted Answer

A)  $x ^ { 2 } - 32 x + 16 = 0$ 
B)  $x ^ { 2 } - 8 x + 56 = 0$ 
C)  $x ^ { 2 } - 64 x + 96 = 0$ 
D)  $x ^ { 2 } - 16 x + 32 = 0$ 
A)  $x ^ { 2 } - 32 x + 16 = 0$ 
B)  $x ^ { 2 } - 8 x + 56 = 0$ 
C)  $x ^ { 2 } - 64 x + 96 = 0$ 
D)  $x ^ { 2 } - 16 x + 32 = 0$

Question 10

Solve the problem.
-A rectangular Persian carpet has a perimeter of 208 inches. The length of the carpet is 18 in. more than the width. What are the dimensions of the carpet?

Accepted Answer

A)  Width: 61 in.; length: 79 in. 
B)  Width: 43 in.; length: 61 in. 
C)  Width: 95 in.; length: 113 in. 
D)  Width: 86 in.; length: 104 in. 
A)  Width: 61 in.; length: 79 in. 
B)  Width: 43 in.; length: 61 in. 
C)  Width: 95 in.; length: 113 in. 
D)  Width: 86 in.; length: 104 in.

Question 11

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$5 ( 2 x - 31 ) = 10 x - 155$$

Accepted Answer

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

Question 12

Solve the problem.
-Roberto invested some money at 2.5%, and then invested $4000 more than twice this amount at 3%. His total annual income from the two investments was $970.00. How much was invested at 3%?

Accepted Answer

A)  $12,000 
B)  $24,000 
C)  $2400 
D)  $20,000 
A)  $12,000 
B)  $24,000 
C)  $2400 
D)  $20,000

Question 13

Multiply or divide, as indicated. Simplify the answer.
-$\sqrt { - 13 } \cdot \sqrt { - 13 }$

Accepted Answer

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

Question 14

Solve the equation using the quadratic formula.
-$$( x + 1 ) ( x - 4 ) = 2$$

Accepted Answer

A)  $\left\{ \frac { 3 } { 2 } \pm \frac { \mathrm { i } \sqrt { 33 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 3 \pm \sqrt { 33 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 3 \pm \sqrt { 33 } } { 2 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 2 } \pm \frac { \mathrm { i } \sqrt { 33 } } { 2 } \right\}$ 
A)  $\left\{ \frac { 3 } { 2 } \pm \frac { \mathrm { i } \sqrt { 33 } } { 2 } \right\}$ 
B)  $\left\{ \frac { - 3 \pm \sqrt { 33 } } { 2 } \right\}$ 
C)  $\left\{ \frac { 3 \pm \sqrt { 33 } } { 2 } \right\}$ 
D)  $\left\{ - \frac { 3 } { 2 } \pm \frac { \mathrm { i } \sqrt { 33 } } { 2 } \right\}$

Question 15

Solve the problem.
-Your home state uses a linear model $y = 34 ( x - 70 ) + 4182$ to predict the number of vacationers $( y )$ as compared to the average temperature for that week $( x )$. Find the number of vacationers predicted for a week with an average temperature of 72 degrees.

Accepted Answer

A)  142,256 vacationers 
B)  9010 vacationers 
C)  4250 vacationers 
D)  6560 vacationers 
A)  142,256 vacationers 
B)  9010 vacationers 
C)  4250 vacationers 
D)  6560 vacationers

Question 16

Solve for y.
-$$7 x - 5 y = 2$$

Accepted Answer

A)  $y = \frac { 7 x + 2 } { 5 }$ 
B)  $y = 7 x - 7$ 
C)  $y = 7 x + 7$ 
D)  $y = \frac { 7 x - 2 } { 5 }$ 
A)  $y = \frac { 7 x + 2 } { 5 }$ 
B)  $y = 7 x - 7$ 
C)  $y = 7 x + 7$ 
D)  $y = \frac { 7 x - 2 } { 5 }$

Question 17

Decide whether the statement is true or false.
--3 is a solution of 2x + 2 = -5.

Accepted Answer

A) True 
 B)False

Question 18

Find the quotient. Write the answer in standard form.
-$$\frac { 2 - 6 i } { 8 + 2 i }$$

Accepted Answer

A)  $\frac { 7 } { 15 } + \frac { 13 } { 60 } \mathrm { i }$ 
B)  $\frac { 1 } { 17 } - \frac { 13 } { 17 }$ i 
C)  $\frac { 1 } { 60 } + \frac { 13 } { 60 } \mathrm { i }$ 
D)  $\frac { 28 } { 17 } + \frac { 44 } { 17 } \mathrm { i }$ 
A)  $\frac { 7 } { 15 } + \frac { 13 } { 60 } \mathrm { i }$ 
B)  $\frac { 1 } { 17 } - \frac { 13 } { 17 }$ i 
C)  $\frac { 1 } { 60 } + \frac { 13 } { 60 } \mathrm { i }$ 
D)  $\frac { 28 } { 17 } + \frac { 44 } { 17 } \mathrm { i }$

Question 19

Find the quotient. Write the answer in standard form.
-$$\frac { 3 - 8 i } { 5 - 6 i }$$

Accepted Answer

A)  $- \frac { 33 } { 61 } + \frac { 58 } { 61 } i$ 
B)  $3 - 2 \mathrm { i }$ 
C)  $- \frac { 63 } { 11 } - 2 i$ 
D)  $\frac { 63 } { 61 } - \frac { 22 } { 61 } \mathrm { i }$ 
A)  $- \frac { 33 } { 61 } + \frac { 58 } { 61 } i$ 
B)  $3 - 2 \mathrm { i }$ 
C)  $- \frac { 63 } { 11 } - 2 i$ 
D)  $\frac { 63 } { 61 } - \frac { 22 } { 61 } \mathrm { i }$

Question 20

Solve the problem.
-A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Accepted Answer

A)  2.2 ft 
B)  1.5 ft 
C)  3 ft 
D)  1 ft 
A)  2.2 ft 
B)  1.5 ft 
C)  3 ft 
D)  1 ft

Solve for y. - $5 x + 8 = 6 y - 9$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 5 } { 8 } - \frac { 1 } { 9 } x \right| > \frac { 2 } { 11 }$

Solve the equation. - $| 7 x + 6 | = | 6 x + 3 |$

Solve the problem. -In triangle ABC, the angle C is six times as large as angle A. The measure of angle B is 28° greater than that of angle A. Find the measure of the angles.

Find the product. Write the answer in standard form. - $( \sqrt { 2 } + 8 i ) ( \sqrt { 2 } - 8 i )$

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $\sqrt { - 13 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\left( x ^ { 2 } + 2 \right) ^ { 1 / 2 } - ( 2 x + 5 ) ^ { 1 / 2 } = 0$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 2 } { ( x + 7 ) ^ { 2 } } < 0$

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. - $8 + 4 \sqrt { 2 } , 8 - 4 \sqrt { 2 }$

Solve the problem. -A rectangular Persian carpet has a perimeter of 208 inches. The length of the carpet is 18 in. more than the width. What are the dimensions of the carpet?

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $5 ( 2 x - 31 ) = 10 x - 155$

Solve the problem. -Roberto invested some money at 2.5%, and then invested $4000 more than twice this amount at 3%. His total annual income from the two investments was $970.00. How much was invested at 3%?

Multiply or divide, as indicated. Simplify the answer. - $\sqrt { - 13 } \cdot \sqrt { - 13 }$

Solve the equation using the quadratic formula. - $( x + 1 ) ( x - 4 ) = 2$

Solve the problem. -Your home state uses a linear model $y = 34 ( x - 70 ) + 4182$ to predict the number of vacationers $( y )$ as compared to the average temperature for that week $( x )$ . Find the number of vacationers predicted for a week with an average temperature of 72 degrees.

Solve for y. - $7 x - 5 y = 2$

Decide whether the statement is true or false. --3 is a solution of 2x + 2 = -5.

Find the quotient. Write the answer in standard form. - $\frac { 2 - 6 i } { 8 + 2 i }$

Find the quotient. Write the answer in standard form. - $\frac { 3 - 8 i } { 5 - 6 i }$

Solve the problem. -A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

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 for y. - 5x+8=6y−95 x + 8 = 6 y - 95x+8=6y−9

Solve the inequality. Write the solution set in interval notation. - ∣58−19x∣>211\left| \frac { 5 } { 8 } - \frac { 1 } { 9 } x \right| > \frac { 2 } { 11 }​85​−91​x​>112​

Solve the equation. - ∣7x+6∣=∣6x+3∣| 7 x + 6 | = | 6 x + 3 |∣7x+6∣=∣6x+3∣