Question 1

Solve the formula for the indicated variable.
-$\mathrm { R } = \mathrm { nE } - \mathrm { nr }$, for $\mathrm { n }$

Accepted Answer

A)  $\mathrm { n } = \frac { \mathrm { R } + \mathrm { nr } } { \mathrm { E } }$ 
B)  $n = R + n r - E$ 
C)  $n = \frac { R } { E - r }$ 
D)  $n = R - E + r$ 
A)  $\mathrm { n } = \frac { \mathrm { R } + \mathrm { nr } } { \mathrm { E } }$ 
B)  $n = R + n r - E$ 
C)  $n = \frac { R } { E - r }$ 
D)  $n = R - E + r$

Question 2

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 3 } { x - 9 } + \frac { 7 } { x + 6 } = \frac { 5 } { x ^ { 2 } - 3 x - 54 }$$

Accepted Answer

A)  $\left\{ \frac { 65 } { 7 } \right\}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ - \frac { 16 } { 3 } \right\}$ 
D)  $\varnothing$ 
A)  $\left\{ \frac { 65 } { 7 } \right\}$ 
B)  $\{ 5 \}$ 
C)  $\left\{ - \frac { 16 } { 3 } \right\}$ 
D)  $\varnothing$

Question 3

Solve the equation.
-$$x ^ { 2 } = 20$$

Accepted Answer

A)  $\pm 4 \mathrm { i } \sqrt { 5 }$ 
B)  $\pm 2 \mathrm { i } \sqrt { 5 }$ 
C)  $\pm 4 \sqrt { 5 }$ 
D)  $\pm 2 \sqrt { 5 }$ 
A)  $\pm 4 \mathrm { i } \sqrt { 5 }$ 
B)  $\pm 2 \mathrm { i } \sqrt { 5 }$ 
C)  $\pm 4 \sqrt { 5 }$ 
D)  $\pm 2 \sqrt { 5 }$

Question 4

Solve and graph the inequality. Give answer in interval notation.
-$$- 1 \leq \frac { x + 1 } { - 2 } \leq 3$$

Accepted Answer

A)  $[ - 7,1 ]$
  
B)  $( - 3,5 )$
  
C)  $[ - 5,3 ]$
  
D)  $( - 1,7 )$
  
A)  $[ - 7,1 ]$
  
B)  $( - 3,5 )$
  
C)  $[ - 5,3 ]$
  
D)  $( - 1,7 )$

Question 5

Solve the equation.
-$$\frac { x - 8 } { 2 } = \frac { x + 8 } { 7 }$$

Accepted Answer

A)  $\left\{ \frac { 24 } { 5 } \right\}$ 
B)  $\left\{ \frac { 72 } { 5 } \right\}$ 
C)  $\{ 8 \}$ 
D)  $\{ - 8 \}$ 
A)  $\left\{ \frac { 24 } { 5 } \right\}$ 
B)  $\left\{ \frac { 72 } { 5 } \right\}$ 
C)  $\{ 8 \}$ 
D)  $\{ - 8 \}$

Question 6

Write the inequality in interval notation.
-$$- 4 < x < - 3$$

Accepted Answer

A)  $[ - 4 , - 3 ]$ 
B)  $[ - 4 , - 3 )$ 
C)  $( - 4 , - 3 )$ 
D)  $( - 4 , - 3 ]$ 
A)  $[ - 4 , - 3 ]$ 
B)  $[ - 4 , - 3 )$ 
C)  $( - 4 , - 3 )$ 
D)  $( - 4 , - 3 ]$

Question 7

Determine whether or not the equation is linear.
-7x + 3x = 0

Accepted Answer

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

Question 8

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$\sqrt { 10 }$

Accepted Answer

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

Question 9

Solve the equation.
-$$x ^ { 2 } - 11 = 0$$

Accepted Answer

A)  $\pm \mathrm { i } \sqrt { 11 }$ 
B)  $\pm \sqrt { 11 }$ 
C)  $\pm 11$ 
D)  $\pm 11 \mathrm { i }$ 
A)  $\pm \mathrm { i } \sqrt { 11 }$ 
B)  $\pm \sqrt { 11 }$ 
C)  $\pm 11$ 
D)  $\pm 11 \mathrm { i }$

Question 10

Solve the problem.
-A chemist needs 120 milliliters of a 69% solution but has only 61% and 73% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

A)  70 mL of 61%; 50 mL of 73% 
B)  50 mL of 61%; 70 mL of 73% 
C)  40 mL of 61%; 80 mL of 73% 
D)  80 mL of 61%; 40 mL of 73% 
A)  70 mL of 61%; 50 mL of 73% 
B)  50 mL of 61%; 70 mL of 73% 
C)  40 mL of 61%; 80 mL of 73% 
D)  80 mL of 61%; 40 mL of 73%

Question 11

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 1$$

Accepted Answer

A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 11 } { 2 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\varnothing$ 
A)  $\{ 0 \}$ 
B)  $\left\{ \frac { 11 } { 2 } \right\}$ 
C)  $\{ 1 \}$ 
D)  $\varnothing$

Question 12

Solve the problem.
-The area of a square is numerically 4 less than the perimeter. Find the length of the side, if the side is greater than 1.

Accepted Answer

A)  9 units 
B)  5 units 
C)  8 units 
D)  2 units 
A)  9 units 
B)  5 units 
C)  8 units 
D)  2 units

Question 13

Decide what values of the variable cannot possibly be solutions for the equation.
-$$3 x ^ { - 2 } + 18 x ^ { - 1 } + 15 = 0$$

Accepted Answer

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

Question 14

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 1 } { x + 20 } > 0$$

Accepted Answer

A)  $[ 20 , \infty ]$ 
B)  $( - 20 , \infty )$ 
C)  $( - \infty , 20 )$ 
D)  $( 20 , - \infty )$ 
A)  $[ 20 , \infty ]$ 
B)  $( - 20 , \infty )$ 
C)  $( - \infty , 20 )$ 
D)  $( 20 , - \infty )$

Question 15

Find the product. Write the answer in standard form.
-$$( 4 - 3 i ) ( 4 + 5 i )$$

Accepted Answer

A)  $- 15 i ^ { 2 } + 8 i - 16$ 
B)  $31 - 8 \mathrm { i }$ 
C)  $1 - 32 \mathrm { i }$ 
D)  $31 + 8 \mathrm { i }$ 
A)  $- 15 i ^ { 2 } + 8 i - 16$ 
B)  $31 - 8 \mathrm { i }$ 
C)  $1 - 32 \mathrm { i }$ 
D)  $31 + 8 \mathrm { i }$

Question 16

Solve the equation for the indicated variable. Assume no denominator is 0.
-$\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$, for $\mathrm { r }$

Accepted Answer

A)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \text { hd } }$ 
B)  $r = \frac { \pm \mathrm { M } \sqrt { \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
C)  $r = \frac { \pm \sqrt { \mathrm { M } \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
D)  $r = \pm \sqrt { \pi M h d }$ 
A)  $r = \frac { \pm \sqrt { \pi \mathrm { Mhd } } } { \text { hd } }$ 
B)  $r = \frac { \pm \mathrm { M } \sqrt { \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
C)  $r = \frac { \pm \sqrt { \mathrm { M } \pi \mathrm { hd } } } { \pi \mathrm { hd } }$ 
D)  $r = \pm \sqrt { \pi M h d }$

Question 17

Decide whether the statement is true or false.
-1 is a solution of -7x - 6 = -13.

Accepted Answer

A) True 
 B)False

Question 18

Solve the inequality. Write the solution set in interval notation.
-$$| 7 + 7 x | > 8$$

Accepted Answer

A)  $\left( - \frac { 15 } { 7 } , \frac { 1 } { 7 } \right)$ 
B)  $\left( - \infty , - \frac { 15 } { 7 } \right) \cup \left( \frac { 1 } { 7 } , \infty \right)$ 
C)  $\left( \frac { 1 } { 7 } , \frac { 15 } { 7 } \right)$ 
D)  $\left\{ - \infty , \frac { 1 } { 7 } \right) \cup \left( \frac { 17 } { 7 } , \infty \right)$ 
A)  $\left( - \frac { 15 } { 7 } , \frac { 1 } { 7 } \right)$ 
B)  $\left( - \infty , - \frac { 15 } { 7 } \right) \cup \left( \frac { 1 } { 7 } , \infty \right)$ 
C)  $\left( \frac { 1 } { 7 } , \frac { 15 } { 7 } \right)$ 
D)  $\left\{ - \infty , \frac { 1 } { 7 } \right) \cup \left( \frac { 17 } { 7 } , \infty \right)$

Question 19

Write the inequality in interval notation.
-$$6 < x \leq 8$$

Accepted Answer

A)  $[ 6,8 )$ 
B)  $( 6,8 ]$ 
C)  $[ 6,8 ]$ 
D)  $( 6,8 )$ 
A)  $[ 6,8 )$ 
B)  $( 6,8 ]$ 
C)  $[ 6,8 ]$ 
D)  $( 6,8 )$

Question 20

Solve the inequality. Write the solution set in interval notation.
-$$2 + \left| 1 - \frac { 1 } { 2 } x \right| \geq 5$$

Accepted Answer

A)  $( - \infty , - 4 ] \cup [ 8 , \infty )$ 
B)  $[ - 8,4 ]$ 
C)  $[ - 4,8 ]$ 
D)  $( - \infty , - 8 ] \cup [ 4 , \infty )$ 
A)  $( - \infty , - 4 ] \cup [ 8 , \infty )$ 
B)  $[ - 8,4 ]$ 
C)  $[ - 4,8 ]$ 
D)  $( - \infty , - 8 ] \cup [ 4 , \infty )$

Solve the formula for the indicated variable. - $\mathrm { R } = \mathrm { nE } - \mathrm { nr }$ , for $\mathrm { n }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 3 } { x - 9 } + \frac { 7 } { x + 6 } = \frac { 5 } { x ^ { 2 } - 3 x - 54 }$

Solve the equation. - $x ^ { 2 } = 20$

Solve and graph the inequality. Give answer in interval notation. - $- 1 \leq \frac { x + 1 } { - 2 } \leq 3$ $Solve and graph the inequality. Give answer in interval notation. - - 1 \leq \frac { x + 1 } { - 2 } \leq 3$

Solve the equation. - $\frac { x - 8 } { 2 } = \frac { x + 8 } { 7 }$

Write the inequality in interval notation. - $- 4 < x < - 3$

Determine whether or not the equation is linear. -7x + 3x = 0

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $\sqrt { 10 }$

Solve the equation. - $x ^ { 2 } - 11 = 0$

Solve the problem. -A chemist needs 120 milliliters of a 69% solution but has only 61% and 73% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 10 + x } + \sqrt { 11 - 5 x } = - 1$

Solve the problem. -The area of a square is numerically 4 less than the perimeter. Find the length of the side, if the side is greater than 1.

Decide what values of the variable cannot possibly be solutions for the equation. - $3 x ^ { - 2 } + 18 x ^ { - 1 } + 15 = 0$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 1 } { x + 20 } > 0$

Find the product. Write the answer in standard form. - $( 4 - 3 i ) ( 4 + 5 i )$

Solve the equation for the indicated variable. Assume no denominator is 0. - $\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$ , for $\mathrm { r }$

Decide whether the statement is true or false. -1 is a solution of -7x - 6 = -13.

Solve the inequality. Write the solution set in interval notation. - $| 7 + 7 x | > 8$

Write the inequality in interval notation. - $6 < x \leq 8$

Solve the inequality. Write the solution set in interval notation. - $2 + \left| 1 - \frac { 1 } { 2 } x \right| \geq 5$

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 formula for the indicated variable. - R=nE−nr\mathrm { R } = \mathrm { nE } - \mathrm { nr }R=nE−nr , for n\mathrm { n }n

Decide what values of the variable cannot possibly be solutions for the equation. - 3x−9+7x+6=5x2−3x−54\frac { 3 } { x - 9 } + \frac { 7 } { x + 6 } = \frac { 5 } { x ^ { 2 } - 3 x - 54 }x−93​+x+67​=x2−3x−545​

Solve the equation. - x2=20x ^ { 2 } = 20x2=20

Solve and graph the inequality. Give answer in interval notation. - −1≤x+1−2≤3- 1 \leq \frac { x + 1 } { - 2 } \leq 3−1≤−2x+1​≤3

Solve the equation. - x−82=x+87\frac { x - 8 } { 2 } = \frac { x + 8 } { 7 }2x−8​=7x+8​

Write the inequality in interval notation. - −4<x<−3- 4 < x < - 3−4<x<−3