Question 1

Solve the equation.
-$$\frac { x + 8 } { 7 } = \frac { x + 9 } { 9 }$$

Accepted Answer

A)  $\left\{ - \frac { 9 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 9 } { 16 } \right\}$ 
C)  $\left\{ \frac { 55 } { 2 } \right\}$ 
D)  $\left\{ \frac { 135 } { 2 } \right\}$ 
A)  $\left\{ - \frac { 9 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 9 } { 16 } \right\}$ 
C)  $\left\{ \frac { 55 } { 2 } \right\}$ 
D)  $\left\{ \frac { 135 } { 2 } \right\}$

Question 2

Write the statement as an absolute value inequality.
-$\mathrm { z }$ is no less than 6 units from 20

Accepted Answer

A)  $| z - 20 | \leq 6$ 
B)  $| z - 6 | > 20$ 
C)  $| z - 20 | \geq 6$ 
D)  $| z - 20 | > 6$ 
A)  $| z - 20 | \leq 6$ 
B)  $| z - 6 | > 20$ 
C)  $| z - 20 | \geq 6$ 
D)  $| z - 20 | > 6$

Question 3

Solve the equation.
-$$x + 7 = 0$$

Accepted Answer

A)  $\mathrm { i } \sqrt { 7 }$ 
B)  $- \mathrm { i } \sqrt { 7 }$ 
C)  $- 7$ 
D)  7 
A)  $\mathrm { i } \sqrt { 7 }$ 
B)  $- \mathrm { i } \sqrt { 7 }$ 
C)  $- 7$ 
D)  7

Question 4

Solve the equation for the indicated variable. Assume no denominator is 0.
-$2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1$, for $y$

Accepted Answer

A)  $y = \frac { 2 x \pm \sqrt { 6 - 4 x ^ { 2 } } } { 3 }$ 
B)  $y = \frac { 2 x \pm \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
C)  $y = \frac { 2 x \pm 4 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
D)  $y = \frac { 2 x \pm 2 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
A)  $y = \frac { 2 x \pm \sqrt { 6 - 4 x ^ { 2 } } } { 3 }$ 
B)  $y = \frac { 2 x \pm \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
C)  $y = \frac { 2 x \pm 4 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$ 
D)  $y = \frac { 2 x \pm 2 \sqrt { 3 - 2 x ^ { 2 } } } { 3 }$

Question 5

Graph the solution set.
-$$| x | = 1$$

Accepted Answer

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

Question 6

Solve the problem.
-Frank can type a report in 6 hours. James takes 7 hours to type it. How long will it take the two of them typing together?

Accepted Answer

A)  $42 \mathrm { hr }$ 
B)  $\frac { 1 } { 13 } \mathrm { hr }$ 
C)  $\frac { 1 } { 42 } \mathrm { hr }$ 
D)  $\frac { 42 } { 13 } \mathrm { hr }$ 
A)  $42 \mathrm { hr }$ 
B)  $\frac { 1 } { 13 } \mathrm { hr }$ 
C)  $\frac { 1 } { 42 } \mathrm { hr }$ 
D)  $\frac { 42 } { 13 } \mathrm { hr }$

Question 7

Solve the problem.
-The position of an object moving in a straight line is given by $s = 2 t ^ { 2 } - 3 t$, where $s$ is in meters and $t$ is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 5 meters?

Accepted Answer

A)  $2.3 \mathrm { sec }$ 
B)  $3.5 \mathrm { sec }$ 
C)  $6.0 \mathrm { sec }$ 
D)  $2.5 \mathrm { sec }$ 
A)  $2.3 \mathrm { sec }$ 
B)  $3.5 \mathrm { sec }$ 
C)  $6.0 \mathrm { sec }$ 
D)  $2.5 \mathrm { sec }$

Question 8

Solve the equation.
-$$1 - \frac { 5 } { 7 x } = \frac { 2 } { 10 }$$

Accepted Answer

A)  $\left\{ - \frac { 25 } { 4 } \right\}$ 
B)  $\left\{ \frac { 25 } { 28 } \right\}$ 
C)  $\left\{ - \frac { 25 } { 28 } \right\}$ 
D)  $\{ - 50 \}$ 
A)  $\left\{ - \frac { 25 } { 4 } \right\}$ 
B)  $\left\{ \frac { 25 } { 28 } \right\}$ 
C)  $\left\{ - \frac { 25 } { 28 } \right\}$ 
D)  $\{ - 50 \}$

Question 9

Write the inequality in interval notation.
-$- 2 < x$

Accepted Answer

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

Question 10

Solve the formula for the indicated variable.
-$V = \frac { 1 } { 3 } B h$, for $h$

Accepted Answer

A)  $h = \frac { 3 B } { V }$ 
B)  $h = \frac { V } { 3 B }$ 
C)  $h = \frac { 3 V } { B }$ 
D)  $h = \frac { B } { 3 V }$ 
A)  $h = \frac { 3 B } { V }$ 
B)  $h = \frac { V } { 3 B }$ 
C)  $h = \frac { 3 V } { B }$ 
D)  $h = \frac { B } { 3 V }$

Question 11

Solve the equation.
-$$\frac { x } { x - 6 } - \frac { 6 } { x + 6 } = \frac { 72 } { x ^ { 2 } - 36 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ \pm 6 \mathrm { i } \}$ 
C)  $\{ \pm 6 \}$ 
D)  $\left\{ \frac { 1 } { 6 } \right\}$ 
A)  $\varnothing$ 
B)  $\{ \pm 6 \mathrm { i } \}$ 
C)  $\{ \pm 6 \}$ 
D)  $\left\{ \frac { 1 } { 6 } \right\}$

Question 12

Solve the equation.
-$$\frac { 5 x } { 7 } - 8 = x$$

Accepted Answer

A)  $\{ 56 \}$ 
B)  $\{ - 28 \}$ 
C)  $\{ 112 \}$ 
D)  $\{ 28 \}$ 
A)  $\{ 56 \}$ 
B)  $\{ - 28 \}$ 
C)  $\{ 112 \}$ 
D)  $\{ 28 \}$

Question 13

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

Accepted Answer

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

Question 14

Solve the equation by the square root property.
-$$x ^ { 2 } = 12$$

Accepted Answer

A)  $\{ \sqrt { 12 } \}$ 
B)  $\{ 144 \}$ 
C)  $\{ \pm 2 \sqrt { 3 } \}$ 
D)  $\{ 6 \}$ 
A)  $\{ \sqrt { 12 } \}$ 
B)  $\{ 144 \}$ 
C)  $\{ \pm 2 \sqrt { 3 } \}$ 
D)  $\{ 6 \}$

Question 15

Solve the equation.
-$$| - 8 + 3 x | = | 7 - 4 x |$$

Accepted Answer

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

Question 16

Solve the equation.
-$\frac { 8 x } { x - 8 } - \frac { 4 } { x } = \frac { 32 } { x ^ { 2 } - 8 x }$

Accepted Answer

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

Question 17

Solve the problem.
-The cost of producing $t$ units is $C = 4 t ^ { 2 } + 6 t$, and the revenue generated from sales is $R = 5 t ^ { 2 } + t$. Determine the number of units to be sold in order to generate a profit.

Accepted Answer

A)  $t > 6$ 
B)  $t > 5$ 
C)  $t > 0$ 
D)  $t > 7$ 
A)  $t > 6$ 
B)  $t > 5$ 
C)  $t > 0$ 
D)  $t > 7$

Question 18

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 1 } { 2 x } + \frac { 6 } { x } = 11$$

Accepted Answer

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

Question 19

Solve the problem.
-The difference of the squares of two positive consecutive even integers is 124 . Find the integers.

Accepted Answer

A)  28,26 
B)  32,34 
C)  30,32 
D)  30,28 
A)  28,26 
B)  32,34 
C)  30,32 
D)  30,28

Question 20

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

Accepted Answer

A)  $y = \frac { 6 x - 8 } { 5 }$ 
B)  $y = 13 - 6 x$ 
C)  $y = 13 + 6 x$ 
D)  $y = \frac { 6 x + 8 } { 5 }$ 
A)  $y = \frac { 6 x - 8 } { 5 }$ 
B)  $y = 13 - 6 x$ 
C)  $y = 13 + 6 x$ 
D)  $y = \frac { 6 x + 8 } { 5 }$

Solve the equation. - $\frac { x + 8 } { 7 } = \frac { x + 9 } { 9 }$

Write the statement as an absolute value inequality. - $\mathrm { z }$ is no less than 6 units from 20

Solve the equation. - $x + 7 = 0$

Solve the equation for the indicated variable. Assume no denominator is 0. - $2 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 1$ , for $y$

Graph the solution set. - $| x | = 1$

Solve the problem. -Frank can type a report in 6 hours. James takes 7 hours to type it. How long will it take the two of them typing together?

Solve the problem. -The position of an object moving in a straight line is given by $s = 2 t ^ { 2 } - 3 t$ , where $s$ is in meters and $t$ is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move 5 meters?

Solve the equation. - $1 - \frac { 5 } { 7 x } = \frac { 2 } { 10 }$

Write the inequality in interval notation. - $- 2 < x$

Solve the formula for the indicated variable. - $V = \frac { 1 } { 3 } B h$ , for $h$

Solve the equation. - $\frac { x } { x - 6 } - \frac { 6 } { x + 6 } = \frac { 72 } { x ^ { 2 } - 36 }$

Solve the equation. - $\frac { 5 x } { 7 } - 8 = x$

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

Solve the equation by the square root property. - $x ^ { 2 } = 12$

Solve the equation. - $| - 8 + 3 x | = | 7 - 4 x |$

Solve the equation. - $\frac { 8 x } { x - 8 } - \frac { 4 } { x } = \frac { 32 } { x ^ { 2 } - 8 x }$

Solve the problem. -The cost of producing $t$ units is $C = 4 t ^ { 2 } + 6 t$ , and the revenue generated from sales is $R = 5 t ^ { 2 } + t$ . Determine the number of units to be sold in order to generate a profit.

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { 2 x } + \frac { 6 } { x } = 11$

Solve the problem. -The difference of the squares of two positive consecutive even integers is 124 . Find the integers.

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

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

Review of Basic Concepts

Filters

Exam 1: Equations and Inequalities

Solve the equation. - x+87=x+99\frac { x + 8 } { 7 } = \frac { x + 9 } { 9 }7x+8​=9x+9​

Write the statement as an absolute value inequality. - z\mathrm { z }z is no less than 6 units from 20

Solve the equation. - x+7=0x + 7 = 0x+7=0

Solve the equation for the indicated variable. Assume no denominator is 0. - 2x2−4xy+3y2=12 x ^ { 2 } - 4 x y + 3 y ^ { 2 } = 12x2−4xy+3y2=1 , for yyy

Graph the solution set. - ∣x∣=1| x | = 1∣x∣=1