Question 1

Solve for y.
-$$9 x + 2 y = 5$$

Accepted Answer

A)  $y = \frac { 7 } { 9 x }$ 
B)  $y = 9 + 9 x$ 
C)  $y = 7 - 9 x$ 
D)  $y = \frac { 5 - 9 x } { 2 }$ 
A)  $y = \frac { 7 } { 9 x }$ 
B)  $y = 9 + 9 x$ 
C)  $y = 7 - 9 x$ 
D)  $y = \frac { 5 - 9 x } { 2 }$

Question 2

Solve for the indicated variable.
-$\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$, for $\mathrm { r }$

Accepted Answer

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

Question 3

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 8 } { x - 2 } + \frac { 8 } { x + 2 } = 3$$

Accepted Answer

A)  $\left\{ \frac { 2 } { 3 } , - 6 \right\}$ 
B)  $\left\{ - \frac { 2 } { 3 } , 6 \right\}$ 
C)  $\left\{ - \frac { 3 } { 2 } , - 6 \right\}$ 
D)  $\{ 2,6 \}$ 
A)  $\left\{ \frac { 2 } { 3 } , - 6 \right\}$ 
B)  $\left\{ - \frac { 2 } { 3 } , 6 \right\}$ 
C)  $\left\{ - \frac { 3 } { 2 } , - 6 \right\}$ 
D)  $\{ 2,6 \}$

Question 4

Decide what values of the variable cannot possibly be solutions for the equation.
-$$1 - \frac { 7 } { x } - \frac { 30 } { x ^ { 2 } } = 0$$

Accepted Answer

A)  $\{ - 10 , - 3 \}$ 
B)  $\{ 10,3 \}$ 
C)  $\{ - 10,3 \}$ 
D)  $\{ 10 , - 3 \}$ 
A)  $\{ - 10 , - 3 \}$ 
B)  $\{ 10,3 \}$ 
C)  $\{ - 10,3 \}$ 
D)  $\{ 10 , - 3 \}$

Question 5

Solve for y.
-$$9 x = 10 y - 7$$

Accepted Answer

A)  $y = 17 + 9 x$ 
B)  $y = 17 - 9 x$ 
C)  $y = \frac { 9 x - 7 } { 10 }$ 
D)  $y = \frac { 9 x } { }$ + 7 10 
A)  $y = 17 + 9 x$ 
B)  $y = 17 - 9 x$ 
C)  $y = \frac { 9 x - 7 } { 10 }$ 
D)  $y = \frac { 9 x } { }$ + 7 10

Question 6

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 3 } + 4 x ^ { 2 } - 4 x - 16 \geq 0$$

Accepted Answer

A)  $[ - 4,2 ]$ 
B)  $[ - 4 , - 2 ] \cup [ 2 , \infty )$ 
C)  $[ - 4 , \infty )$ 
D)  $[ - 2,2 ] \cup [ 4 , \infty )$ 
A)  $[ - 4,2 ]$ 
B)  $[ - 4 , - 2 ] \cup [ 2 , \infty )$ 
C)  $[ - 4 , \infty )$ 
D)  $[ - 2,2 ] \cup [ 4 , \infty )$

Question 7

Write the statement as an absolute value inequality.
-$\mathrm { x }$ is within 3 units of 2

Accepted Answer

A)  $| x - 3 | < 2$ 
B)  $| x - 2 | < 3$ 
C)  $| 3 - x | < 2$ 
D)  $| x - 2 | \leq 3$ 
A)  $| x - 3 | < 2$ 
B)  $| x - 2 | < 3$ 
C)  $| 3 - x | < 2$ 
D)  $| x - 2 | \leq 3$

Question 8

Solve the rational inequality. Write the solution set in interval notation.
-The profit made when t units are sold, t > 0, is given by $\mathrm { P } = \mathrm { t } ^ { 2 } - 30 \mathrm { t } + 216$ Determine the number of units to be sold in order for P > 0 (a profit is made).

Accepted Answer

A) t > 18 or t < 12 B) 18 < t < 12 C) t = 30 D) t = 18 or t = 12 A) t > 18 or t < 12 B) 18 < t < 12 C) t = 30 D) t = 18 or t = 12

Question 9

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { x + 6 } + \sqrt { 2 - x } = 4$$

Accepted Answer

A)  $\{ 2 , - 2 \}$ 
B)  $\{ 0 \}$ 
C)  $\{ \sqrt { 31 } , - 2 \}$ 
D)  $\{ - 2 \}$ 
A)  $\{ 2 , - 2 \}$ 
B)  $\{ 0 \}$ 
C)  $\{ \sqrt { 31 } , - 2 \}$ 
D)  $\{ - 2 \}$

Question 10

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\sqrt { 8 x - 5 } - \sqrt { 3 x + 9 } = 0$$

Accepted Answer

A)  $\left\{ \frac { 4 } { 5 } \right\}$ 
B)  $\left\{ \frac { 14 } { 11 } \right\}$ 
C)  $\left\{ \frac { 5 } { 14 } \right\}$ 
D)  $\left\{ \frac { 14 } { 5 } \right\}$ 
A)  $\left\{ \frac { 4 } { 5 } \right\}$ 
B)  $\left\{ \frac { 14 } { 11 } \right\}$ 
C)  $\left\{ \frac { 5 } { 14 } \right\}$ 
D)  $\left\{ \frac { 14 } { 5 } \right\}$

Question 11

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 1 } { 2 x } + \frac { 9 } { x } = 12$$

Accepted Answer

A)  $- 2$ 
B)  0 
C)  1,2 
D)  $0 , - \frac { 1 } { 2 }$ 
A)  $- 2$ 
B)  0 
C)  1,2 
D)  $0 , - \frac { 1 } { 2 }$

Question 12

Solve the problem.
-In a chemistry class, 9 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Accepted Answer

A)  9 L 
B)  5.5 L 
C)  4.5 L 
D)  3.5 L 
A)  9 L 
B)  5.5 L 
C)  4.5 L 
D)  3.5 L

Question 13

Solve the problem
-The sum of the squares of two consecutive even integers is 2452. Find the integers.

Accepted Answer

A)  34,36 or $- 34 , - 36$ 
B)  $- 34 , - 36$ 
C)  34,36 
D)  $35 , - 37$ 
A)  34,36 or $- 34 , - 36$ 
B)  $- 34 , - 36$ 
C)  34,36 
D)  $35 , - 37$

Question 14

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { - 4 x + 6 } { 2 x ^ { 2 } + 2 } > 0$$

Accepted Answer

A)  $\left( - \infty , - \frac { 2 } { 3 } \right)$ 
B)  $\left( - \infty , \frac { 3 } { 2 } \right)$ 
C)  $( - \infty , 0 )$ 
D)  $\left( - \frac { 3 } { 2 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 2 } { 3 } \right)$ 
B)  $\left( - \infty , \frac { 3 } { 2 } \right)$ 
C)  $( - \infty , 0 )$ 
D)  $\left( - \frac { 3 } { 2 } , \infty \right)$

Question 15

Find the sum or difference. Write the answer in standard form.
-$$( 2 + 5 i ) - ( - 4 - 7 i ) - ( - 1 - 3 i )$$

Accepted Answer

A)  $7 + 15 \mathrm { i }$ 
B)  $7 - 5 \mathrm { i }$ 
C)  $5 + 9 \mathrm { i }$ 
D)  $- 3 - 5 \mathrm { i }$ 
A)  $7 + 15 \mathrm { i }$ 
B)  $7 - 5 \mathrm { i }$ 
C)  $5 + 9 \mathrm { i }$ 
D)  $- 3 - 5 \mathrm { i }$

Question 16

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { - 4 } { x - 8 } + \frac { 8 } { x + 8 } = \frac { - 64 } { x ^ { 2 } - 64 }$$

Accepted Answer

A)  $\{ - 8 \}$ 
B)  $\{ - 6 \}$ 
C)  $\varnothing$ 
D)  $\{ 8 \}$ 
A)  $\{ - 8 \}$ 
B)  $\{ - 6 \}$ 
C)  $\varnothing$ 
D)  $\{ 8 \}$

Question 17

Solve the equation.
-$$1 - \frac { 6 } { 8 x } = \frac { 2 } { 5 }$$

Accepted Answer

A)  $\left\{ - \frac { 5 } { 4 } \right\}$ 
B)  $\{ - 10 \}$ 
C)  $\{ - 30 \}$ 
D)  $\left\{ \frac { 5 } { 4 } \right\}$ 
A)  $\left\{ - \frac { 5 } { 4 } \right\}$ 
B)  $\{ - 10 \}$ 
C)  $\{ - 30 \}$ 
D)  $\left\{ \frac { 5 } { 4 } \right\}$

Question 18

Graph the solution set.
-$| x | = 3$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

Decide what values of the variable cannot possibly be solutions for the equation.
-$$6 x ^ { 2 / 5 } + 23 x ^ { 1 / 5 } + 20 = 0$$

Accepted Answer

A)  $\{ 2,3 \}$ 
B)  $\left\{ \frac { 3125 } { 32 } , \frac { 1024 } { 243 } \right\}$ 
C)  $\left\{ - \frac { 3125 } { 32 } , - \frac { 1024 } { 243 } \right\}$ 
D)  $\left\{ - \frac { 5 } { 2 } , - \frac { 4 } { 3 } \right\}$ 
A)  $\{ 2,3 \}$ 
B)  $\left\{ \frac { 3125 } { 32 } , \frac { 1024 } { 243 } \right\}$ 
C)  $\left\{ - \frac { 3125 } { 32 } , - \frac { 1024 } { 243 } \right\}$ 
D)  $\left\{ - \frac { 5 } { 2 } , - \frac { 4 } { 3 } \right\}$

Question 20

Solve the formula for the indicated variable.
-$A = b h$, for $h$

Accepted Answer

A)  $h = A - b$ 
B)  $h = \frac { A } { b }$ 
C)  $h = A b$ 
D)  $h = \frac { b } { A }$ 
A)  $h = A - b$ 
B)  $h = \frac { A } { b }$ 
C)  $h = A b$ 
D)  $h = \frac { b } { A }$

Solve for y. - $9 x + 2 y = 5$

Solve for the indicated variable. - $\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }$ , for $\mathrm { r }$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 8 } { x - 2 } + \frac { 8 } { x + 2 } = 3$

Decide what values of the variable cannot possibly be solutions for the equation. - $1 - \frac { 7 } { x } - \frac { 30 } { x ^ { 2 } } = 0$

Solve for y. - $9 x = 10 y - 7$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } + 4 x ^ { 2 } - 4 x - 16 \geq 0$

Write the statement as an absolute value inequality. - $\mathrm { x }$ is within 3 units of 2

Solve the rational inequality. Write the solution set in interval notation. -The profit made when t units are sold, t > 0, is given by $\mathrm { P } = \mathrm { t } ^ { 2 } - 30 \mathrm { t } + 216$ Determine the number of units to be sold in order for P > 0 (a profit is made).

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { x + 6 } + \sqrt { 2 - x } = 4$

Decide what values of the variable cannot possibly be solutions for the equation. - $\sqrt { 8 x - 5 } - \sqrt { 3 x + 9 } = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { 2 x } + \frac { 9 } { x } = 12$

Solve the problem. -In a chemistry class, 9 liters of a 4% silver iodide solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?

Solve the problem -The sum of the squares of two consecutive even integers is 2452. Find the integers.

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 4 x + 6 } { 2 x ^ { 2 } + 2 } > 0$

Find the sum or difference. Write the answer in standard form. - $( 2 + 5 i ) - ( - 4 - 7 i ) - ( - 1 - 3 i )$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { - 4 } { x - 8 } + \frac { 8 } { x + 8 } = \frac { - 64 } { x ^ { 2 } - 64 }$

Solve the equation. - $1 - \frac { 6 } { 8 x } = \frac { 2 } { 5 }$

Graph the solution set. - $| x | = 3$

Decide what values of the variable cannot possibly be solutions for the equation. - $6 x ^ { 2 / 5 } + 23 x ^ { 1 / 5 } + 20 = 0$

Solve the formula for the indicated variable. - $A = b h$ , for $h$

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. - 9x+2y=59 x + 2 y = 59x+2y=5

Solve for the indicated variable. - M=πr2hd\mathrm { M } = \pi \mathrm { r } ^ { 2 } \mathrm { hd }M=πr2hd , for r\mathrm { r }r

Decide what values of the variable cannot possibly be solutions for the equation. - 8x−2+8x+2=3\frac { 8 } { x - 2 } + \frac { 8 } { x + 2 } = 3x−28​+x+28​=3

Decide what values of the variable cannot possibly be solutions for the equation. - 1−7x−30x2=01 - \frac { 7 } { x } - \frac { 30 } { x ^ { 2 } } = 01−x7​−x230​=0

Solve for y. - 9x=10y−79 x = 10 y - 79x=10y−7

Solve the inequality. Write the solution set in interval notation. - x3+4x2−4x−16≥0x ^ { 3 } + 4 x ^ { 2 } - 4 x - 16 \geq 0x3+4x2−4x−16≥0

Write the statement as an absolute value inequality. - x\mathrm { x }x is within 3 units of 2

Decide what values of the variable cannot possibly be solutions for the equation. - x+6+2−x=4\sqrt { x + 6 } + \sqrt { 2 - x } = 4x+6​+2−x​=4

Decide what values of the variable cannot possibly be solutions for the equation. - 8x−5−3x+9=0\sqrt { 8 x - 5 } - \sqrt { 3 x + 9 } = 08x−5​−3x+9​=0

Decide what values of the variable cannot possibly be solutions for the equation. - 12x+9x=12\frac { 1 } { 2 x } + \frac { 9 } { x } = 122x1​+x9​=12