Question 1

Solve the equation.
-$- 7 [ - 2 x + 4 - 3 ( x + 1 ) ] = - 3 x - 4$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 53 } { 38 } \right\}$ 
C)  $\left\{ \frac { 53 } { 2 } \right\}$ 
D)  $\left\{ \frac { 3 } { 38 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 53 } { 38 } \right\}$ 
C)  $\left\{ \frac { 53 } { 2 } \right\}$ 
D)  $\left\{ \frac { 3 } { 38 } \right\}$

Question 2

Solve for y.
-$$7 x - 6 ( x + y ) = y - x$$

Accepted Answer

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

Question 3

Write the statement as an absolute value inequality.
-The temperatures in a freeze-dry process in degrees Celsius roughly satisfy the inequality $| C + 99 |$ $\leq 64$. What range of temperatures corresponds to this inequality?

Accepted Answer

A)  $\left[ - 35 ^ { \circ } \mathrm { C } , 163 ^ { \circ } \mathrm { C } \right]$ 
B)  $\left[ - 163 ^ { \circ } \mathrm { C } , - 35 ^ { \circ } \mathrm { C } \right]$ 
C)  $\left[ - 35 ^ { \circ } \mathrm { C } , 35 ^ { \circ } \mathrm { C } \right]$ 
D)  $\left[ - 163 ^ { \circ } \mathrm { C } , 163 ^ { \circ } \mathrm { C } \right]$ 
A)  $\left[ - 35 ^ { \circ } \mathrm { C } , 163 ^ { \circ } \mathrm { C } \right]$ 
B)  $\left[ - 163 ^ { \circ } \mathrm { C } , - 35 ^ { \circ } \mathrm { C } \right]$ 
C)  $\left[ - 35 ^ { \circ } \mathrm { C } , 35 ^ { \circ } \mathrm { C } \right]$ 
D)  $\left[ - 163 ^ { \circ } \mathrm { C } , 163 ^ { \circ } \mathrm { C } \right]$

Question 4

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

Accepted Answer

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

Question 5

Multiply or divide, as indicated. Simplify the answer.
-$$\frac { \sqrt { - 10 } } { \sqrt { - 250 } }$$

Accepted Answer

A)  $\frac { 1 } { 5 \mathrm { i } }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $- \frac { 1 } { 5 } \mathrm { i }$ 
D)  $- \frac { 1 } { 5 }$ 
A)  $\frac { 1 } { 5 \mathrm { i } }$ 
B)  $\frac { 1 } { 5 }$ 
C)  $- \frac { 1 } { 5 } \mathrm { i }$ 
D)  $- \frac { 1 } { 5 }$

Question 6

Find the product. Write the answer in standard form.
-$$6 i ( 9 - 6 i )$$

Accepted Answer

A)  $54 \mathrm { i } - 36$ 
B)  $- 54 i - 36 i ^ { 2 }$ 
C)  $54 i + 36 i ^ { 2 }$ 
D)  $36 + 54 \mathrm { i }$ 
A)  $54 \mathrm { i } - 36$ 
B)  $- 54 i - 36 i ^ { 2 }$ 
C)  $54 i + 36 i ^ { 2 }$ 
D)  $36 + 54 \mathrm { i }$

Question 7

Solve the equation by the square root property.
-Only one of the following equations does not require Step 1 of the method for completing the square. Which one is it?

Accepted Answer

A)  $( 3 x + 5 ) ( x - 7 ) = 0$ 
B)  $( 3 x + 5 ) ^ { 2 } = 7$ 
C)  $x ^ { 2 } + x = 7$ 
D)  $3 x ^ { 2 } + 5 x - 7 = 0$ 
A)  $( 3 x + 5 ) ( x - 7 ) = 0$ 
B)  $( 3 x + 5 ) ^ { 2 } = 7$ 
C)  $x ^ { 2 } + x = 7$ 
D)  $3 x ^ { 2 } + 5 x - 7 = 0$

Question 8

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 6 } { x + 5 } = 1 - \frac { 1 } { x - 5 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 0,7 \}$ 
C)  $\{ 0 , - 5 \}$ 
D)  $\{ 1,5 \}$ 
A)  $\varnothing$ 
B)  $\{ 0,7 \}$ 
C)  $\{ 0 , - 5 \}$ 
D)  $\{ 1,5 \}$

Question 9

Decide what values of the variable cannot possibly be solutions for the equation.
-$$6 x ^ { - 2 / 5 } + 13 x ^ { - 1 / 5 } + 6 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 2 } , - \frac { 2 } { 3 } \right\}$ 
B)  $\left\{ \frac { 243 } { 32 } , \frac { 32 } { 243 } \right\}$ 
C)  $\{ 2,3 \}$ 
D)  $\left\{ - \frac { 243 } { 32 } , - \frac { 32 } { 243 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 2 } , - \frac { 2 } { 3 } \right\}$ 
B)  $\left\{ \frac { 243 } { 32 } , \frac { 32 } { 243 } \right\}$ 
C)  $\{ 2,3 \}$ 
D)  $\left\{ - \frac { 243 } { 32 } , - \frac { 32 } { 243 } \right\}$

Question 10

Solve the equation.
-$| - 5 x + 7 | = 4$

Accepted Answer

A)  $\left\{ - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 5 } , - \frac { 3 } { 5 } \right\}$ 
C)  $\left\{ \frac { 3 } { 5 } \right\}$ 
D)  $\left\{ \frac { 3 } { 5 } , \frac { 11 } { 5 } \right\}$ 
A)  $\left\{ - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 5 } , - \frac { 3 } { 5 } \right\}$ 
C)  $\left\{ \frac { 3 } { 5 } \right\}$ 
D)  $\left\{ \frac { 3 } { 5 } , \frac { 11 } { 5 } \right\}$

Question 11

Solve for the indicated variable.
-$V = \frac { 1 } { m } \sqrt { 2 V e m }$, for $m$

Accepted Answer

A)  $m = \frac { 2 V ^ { 3 } } { e }$ 
B)  $m = \frac { 2 V } { e }$ 
C)  $m = \frac { 2 e } { V }$ 
D)  $m = \frac { \pm \sqrt { 2 V e } } { V e }$ 
A)  $m = \frac { 2 V ^ { 3 } } { e }$ 
B)  $m = \frac { 2 V } { e }$ 
C)  $m = \frac { 2 e } { V }$ 
D)  $m = \frac { \pm \sqrt { 2 V e } } { V e }$

Question 12

Solve the equation.
-$$- 6 x - 2 - 2 ( x + 1 ) = - ( - 7 x + 7 )$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 6 } \right\}$ 
C)  $\left\{ \frac { 1 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 11 } { 15 } \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 11 } { 6 } \right\}$ 
C)  $\left\{ \frac { 1 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 11 } { 15 } \right\}$

Question 13

Solve the inequality. Write the solution set in interval notation.
-$| 9 - x | \geq 1$

Accepted Answer

A)  $[ 8,10 ]$ 
B)  $( - \infty , 8 ] \cup [ 10 , \infty )$ 
C)  $[ 10 , \infty )$ 
D)  $[ 8 , \infty )$ 
A)  $[ 8,10 ]$ 
B)  $( - \infty , 8 ] \cup [ 10 , \infty )$ 
C)  $[ 10 , \infty )$ 
D)  $[ 8 , \infty )$

Question 14

Solve the inequality. Write the solution set in interval notation.
-$| - 5 x + 1 | < 4$

Accepted Answer

A)  $\left( - \frac { 3 } { 5 } , 1 \right)$ 
B)  $\left( - \infty , - \frac { 7 } { 5 } \right) \cup \left( \frac { 1 } { 5 } , \infty \right)$ 
C)  $\left( - \frac { 3 } { 5 } , - 1 \right)$ 
D)  $\left( - \infty , - \frac { 3 } { 5 } \right) \cup ( 1 , \infty )$ 
A)  $\left( - \frac { 3 } { 5 } , 1 \right)$ 
B)  $\left( - \infty , - \frac { 7 } { 5 } \right) \cup \left( \frac { 1 } { 5 } , \infty \right)$ 
C)  $\left( - \frac { 3 } { 5 } , - 1 \right)$ 
D)  $\left( - \infty , - \frac { 3 } { 5 } \right) \cup ( 1 , \infty )$

Question 15

Solve the problem.
-A can has a surface area of 831 square inches. Its height is 5.67 inches. What is the radius of the circular top? Round to the nearest hundredth.

Accepted Answer

A)  11.55 in. 
B)  9.01 in. 
C)  23.33 in. 
D)  4.45 in. 
A)  11.55 in. 
B)  9.01 in. 
C)  23.33 in. 
D)  4.45 in.

Question 16

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

Accepted Answer

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

Question 17

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 2 } { 11 x } - 2 = \frac { 3 } { 14 x }$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 308 } \right\}$ 
B)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 5 } { 2 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 308 } \right\}$ 
B)  $\left\{ - \frac { 3 } { 2 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 5 } { 2 } \right\}$

Question 18

Solve the problem.
-A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m longer than the length of the longer leg. How long is the longer leg?

Accepted Answer

A)  180 m 
B)  240 m 
C)  300 m 
D)  360 m 
A)  180 m 
B)  240 m 
C)  300 m 
D)  360 m

Question 19

Find the sum or difference. Write the answer in standard form.
-$$( 6 - 9 i ) + ( 3 + 6 i )$$

Accepted Answer

A)  $- 9 + 3 i$ 
B)  $3 + 15 i$ 
C)  $9 - 3 \mathrm { i }$ 
D)  $9 + 3 \mathrm { i }$ 
A)  $- 9 + 3 i$ 
B)  $3 + 15 i$ 
C)  $9 - 3 \mathrm { i }$ 
D)  $9 + 3 \mathrm { i }$

Question 20

Find the quotient. Write the answer in standard form.
-$$\frac { 7 + 3 i } { 4 - 6 i }$$

Accepted Answer

A)  $- \frac { 1 } { 4 } + \frac { 27 } { 20 } \mathrm { i }$ 
B)  $\frac { 5 } { 26 } + \frac { 27 } { 26 } \mathrm { i }$ 
C)  $\frac { 23 } { 13 } + \frac { 15 } { 13 } \mathrm { i }$ 
D)  $- \frac { 23 } { 10 } + \frac { 27 } { 20 } \mathrm { i }$ 
A)  $- \frac { 1 } { 4 } + \frac { 27 } { 20 } \mathrm { i }$ 
B)  $\frac { 5 } { 26 } + \frac { 27 } { 26 } \mathrm { i }$ 
C)  $\frac { 23 } { 13 } + \frac { 15 } { 13 } \mathrm { i }$ 
D)  $- \frac { 23 } { 10 } + \frac { 27 } { 20 } \mathrm { i }$

Solve the equation. - $- 7 [ - 2 x + 4 - 3 ( x + 1 ) ] = - 3 x - 4$

Solve for y. - $7 x - 6 ( x + y ) = y - x$

Write the statement as an absolute value inequality. -The temperatures in a freeze-dry process in degrees Celsius roughly satisfy the inequality $| C + 99 |$ $\leq 64$ . What range of temperatures corresponds to this inequality?

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

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 10 } } { \sqrt { - 250 } }$

Find the product. Write the answer in standard form. - $6 i ( 9 - 6 i )$

Solve the equation by the square root property. -Only one of the following equations does not require Step 1 of the method for completing the square. Which one is it?

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 6 } { x + 5 } = 1 - \frac { 1 } { x - 5 }$

Decide what values of the variable cannot possibly be solutions for the equation. - $6 x ^ { - 2 / 5 } + 13 x ^ { - 1 / 5 } + 6 = 0$

Solve the equation. - $| - 5 x + 7 | = 4$

Solve for the indicated variable. - $V = \frac { 1 } { m } \sqrt { 2 V e m }$ , for $m$

Solve the equation. - $- 6 x - 2 - 2 ( x + 1 ) = - ( - 7 x + 7 )$

Solve the inequality. Write the solution set in interval notation. - $| 9 - x | \geq 1$

Solve the inequality. Write the solution set in interval notation. - $| - 5 x + 1 | < 4$

Solve the problem. -A can has a surface area of 831 square inches. Its height is 5.67 inches. What is the radius of the circular top? Round to the nearest hundredth.

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

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 2 } { 11 x } - 2 = \frac { 3 } { 14 x }$

Solve the problem. -A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m longer than the length of the longer leg. How long is the longer leg?

Find the sum or difference. Write the answer in standard form. - $( 6 - 9 i ) + ( 3 + 6 i )$

Find the quotient. Write the answer in standard form. - $\frac { 7 + 3 i } { 4 - 6 i }$

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. - −7[−2x+4−3(x+1)]=−3x−4- 7 [ - 2 x + 4 - 3 ( x + 1 ) ] = - 3 x - 4−7[−2x+4−3(x+1)]=−3x−4

Solve for y. - 7x−6(x+y)=y−x7 x - 6 ( x + y ) = y - x7x−6(x+y)=y−x

Write the statement as an absolute value inequality. -The temperatures in a freeze-dry process in degrees Celsius roughly satisfy the inequality ∣C+99∣| C + 99 |∣C+99∣ ≤64\leq 64≤64 . What range of temperatures corresponds to this inequality?

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - π\piπ

Multiply or divide, as indicated. Simplify the answer. - −10−250\frac { \sqrt { - 10 } } { \sqrt { - 250 } }−250​−10​​

Find the product. Write the answer in standard form. - 6i(9−6i)6 i ( 9 - 6 i )6i(9−6i)