Question 1

Decide what values of the variable cannot possibly be solutions for the equation.
-$$x ^ { 4 } + 720 = 89 x ^ { 2 }$$

Accepted Answer

A)  $\{ - 80 , - 9,9,80 \}$ 
B)  $\{ 9,80 \}$ 
C)  $\{ - 4 \sqrt { 5 } , - 3,3,4 \sqrt { 5 } \}$ 
D)  $\{ 3,4 \sqrt { 5 } \}$ 
A)  $\{ - 80 , - 9,9,80 \}$ 
B)  $\{ 9,80 \}$ 
C)  $\{ - 4 \sqrt { 5 } , - 3,3,4 \sqrt { 5 } \}$ 
D)  $\{ 3,4 \sqrt { 5 } \}$

Question 2

Write the inequality in interval notation.
-$$6 > x \geq 3$$

Accepted Answer

A)  $[ 3,6 )$ 
B)  $( 3,6 )$ 
C)  $( 3,6 ]$ 
D)  $[ 3,6 ]$ 
A)  $[ 3,6 )$ 
B)  $( 3,6 )$ 
C)  $( 3,6 ]$ 
D)  $[ 3,6 ]$

Question 3

Find the sum or difference. Write the answer in standard form.
-$i \sqrt { 7 } + 9 - ( 4 + 7 i \sqrt { 7 } ) - ( 9 - i \sqrt { 7 } )$

Accepted Answer

A)  $- 4 - 9 i \sqrt { 7 }$ 
B)  $4 - 9 i \sqrt { 7 }$ 
C)  $- 4 + 5 i \sqrt { 7 }$ 
D)  $- 4 - 5 i \sqrt { 7 }$ 
A)  $- 4 - 9 i \sqrt { 7 }$ 
B)  $4 - 9 i \sqrt { 7 }$ 
C)  $- 4 + 5 i \sqrt { 7 }$ 
D)  $- 4 - 5 i \sqrt { 7 }$

Question 4

Decide what values of the variable cannot possibly be solutions for the equation.
-$$( 10 + x ) ^ { 1 / 2 } + ( 11 - 5 x ) ^ { 1 / 2 } = - 1$$

Accepted Answer

A)  $\left\{ - 1 , \frac { 10 } { 9 } \right\}$ 
B)  $\{ 0 \}$ 
C)  $\varnothing$ 
D)  $\{ 1 \}$ 
A)  $\left\{ - 1 , \frac { 10 } { 9 } \right\}$ 
B)  $\{ 0 \}$ 
C)  $\varnothing$ 
D)  $\{ 1 \}$

Question 5

Solve the equation by completing the square.
-$$8 x ^ { 2 } + 7 x = - 2$$

Accepted Answer

A)  $\left\{ \frac { - 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
B)  $\left\{ \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$ 
C)  $\left\{ \frac { 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$ 
A)  $\left\{ \frac { - 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
B)  $\left\{ \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$ 
C)  $\left\{ \frac { 7 \pm \sqrt { 15 } } { 16 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 16 } \pm \frac { \sqrt { 15 } } { 16 } \mathrm { i } \right\}$

Question 6

Solve and graph the inequality. Give answer in interval notation.
-$$\frac { x - 2 } { 18 } \geq \frac { x - 5 } { 24 } + \frac { 1 } { 72 }$$

Accepted Answer

A)  $( - 6 , \infty )$
  
B)  $( - \infty , - 6 )$
  
C)  $[ - 6 , \infty )$
  
D)  $( - \infty , - 6 ]$
  
A)  $( - 6 , \infty )$
  
B)  $( - \infty , - 6 )$
  
C)  $[ - 6 , \infty )$
  
D)  $( - \infty , - 6 ]$

Question 7

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 8 x + 12 \geq 0$$

Accepted Answer

A)  $[ - 6 , - 2 ]$ 
B)  $[ - 2 , \infty )$ 
C)  $( - \infty , - 6 ]$ 
D)  $( - \infty , - 6 ] \cup [ - 2 , \infty )$ 
A)  $[ - 6 , - 2 ]$ 
B)  $[ - 2 , \infty )$ 
C)  $( - \infty , - 6 ]$ 
D)  $( - \infty , - 6 ] \cup [ - 2 , \infty )$

Question 8

Solve the problem
-Find two consecutive odd integers whose product is 483.

Accepted Answer

A)  21,23 or $- 21 , - 23$ 
B)  $- 21 , - 23$ 
C)  21,23 
D)  $21 , - 23$ 
A)  21,23 or $- 21 , - 23$ 
B)  $- 21 , - 23$ 
C)  21,23 
D)  $21 , - 23$

Question 9

Write the statement as an absolute value inequality.
-In a milling operation, the thickness of the wood panels that can be produced satisfies the inequality $| \mathrm { x } - 1.88 | \leq 1.20$. What range of thicknesses corresponds to this inequality?

Accepted Answer

A)  $[ 0.68,3.08 ]$ 
B)  $[ 0.68,6.16 ]$ 
C)  $[ 0.34,3.08 ]$ 
D)  $[ 1.20,1.88 ]$ 
A)  $[ 0.68,3.08 ]$ 
B)  $[ 0.68,6.16 ]$ 
C)  $[ 0.34,3.08 ]$ 
D)  $[ 1.20,1.88 ]$

Question 10

Solve the problem.
-A triangular shaped lake-front lot has a perimeter of 1200 ft. One side is 100 ft longer than the shortest side, while the third side is 200 ft longer than the shortest side. Find the lengths of all three
Sides.

Accepted Answer

A)  300 ft, 400 ft, 500 ft 
B)  100 ft, 200 ft, 300 ft 
C)  400 ft, 500 ft, 600 ft 
D)  400 ft, 400 ft, 400 ft 
A)  300 ft, 400 ft, 500 ft 
B)  100 ft, 200 ft, 300 ft 
C)  400 ft, 500 ft, 600 ft 
D)  400 ft, 400 ft, 400 ft

Question 11

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 3 x + 2 > 0$$

Accepted Answer

A)  $( - \infty , - 2 )$ 
B)  $( - 1 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
D)  $( - 2 , - 1 )$ 
A)  $( - \infty , - 2 )$ 
B)  $( - 1 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
D)  $( - 2 , - 1 )$

Question 12

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 7 } { x - 4 } = 1 + \frac { 9 } { x + 4 }$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ - 9,10 \}$ 
C)  $\{ 8 , - 10 \}$ 
D)  $\{ - 8,10 \}$ 
A)  $\varnothing$ 
B)  $\{ - 9,10 \}$ 
C)  $\{ 8 , - 10 \}$ 
D)  $\{ - 8,10 \}$

Question 13

Solve for the indicated variable.
-$\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$, for $\mathrm { v }$

Accepted Answer

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

Question 14

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 3 x \leq - 2$$

Accepted Answer

A)  $[ - 2 , - 1 ]$ 
B)  $( - \infty , - 2 ] \cup [ - 1 , \infty )$ 
C)  $( - 2 , - 1 )$ 
D)  $[ 1,2 ]$ 
A)  $[ - 2 , - 1 ]$ 
B)  $( - \infty , - 2 ] \cup [ - 1 , \infty )$ 
C)  $( - 2 , - 1 )$ 
D)  $[ 1,2 ]$

Question 15

Determine whether or not the equation is linear.
-$6 x ^ { 2 } - 5 x + 9 = 0$

Accepted Answer

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

Question 16

Solve the inequality. Write the solution set in interval notation.
-$$\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| < 0$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - 3,3 )$ 
C)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
D)  $\varnothing$ 
A)  $( - \infty , \infty )$ 
B)  $( - 3,3 )$ 
C)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
D)  $\varnothing$

Question 17

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 5 } { x - 1 } - \frac { 8 x } { 1 - x } = 10$$

Accepted Answer

A)  $- 1,1$ 
B)  1 
C)  $- 1,0,1$ 
D)  $- 1,0$ 
A)  $- 1,1$ 
B)  1 
C)  $- 1,0,1$ 
D)  $- 1,0$

Question 18

Find the quotient. Write the answer in standard form.
-$$\frac { 10 } { - i }$$

Accepted Answer

A)  10 
B)  $10 \mathrm { i }$ 
C)  $- 10$ 
D)  $- 10 \mathrm { i }$ 
A)  10 
B)  $10 \mathrm { i }$ 
C)  $- 10$ 
D)  $- 10 \mathrm { i }$

Question 19

Solve the equation.
-$$\left| 9 x ^ { 3 } + 3 x ^ { 2 } - 6 x \right| = 0$$

Accepted Answer

A)  $\left\{ \frac { 3 } { 2 } , 1,0 \right\}$ 
B)  $\left\{ \frac { 3 } { 2 } , 0 \right\}$ 
C)  $\left\{ \frac { 2 } { 3 } , - 1,0 \right\}$ 
D)  $\left\{ \frac { 3 } { 2 } , - 1 \right\}$ 
A)  $\left\{ \frac { 3 } { 2 } , 1,0 \right\}$ 
B)  $\left\{ \frac { 3 } { 2 } , 0 \right\}$ 
C)  $\left\{ \frac { 2 } { 3 } , - 1,0 \right\}$ 
D)  $\left\{ \frac { 3 } { 2 } , - 1 \right\}$

Question 20

Solve the equation by completing the square.
-$$x ^ { 2 } + 4 x + 8 = 0$$

Accepted Answer

A)  $\{ 0 , - 4 \}$ 
B)  $\{ - 2 \pm 2 \sqrt { 2 } \}$ 
C)  $\{ 2 \pm 2 \mathrm { i } \}$ 
D)  $\{ - 2 \pm 2 i \}$ 
A)  $\{ 0 , - 4 \}$ 
B)  $\{ - 2 \pm 2 \sqrt { 2 } \}$ 
C)  $\{ 2 \pm 2 \mathrm { i } \}$ 
D)  $\{ - 2 \pm 2 i \}$

Decide what values of the variable cannot possibly be solutions for the equation. - $x ^ { 4 } + 720 = 89 x ^ { 2 }$

Write the inequality in interval notation. - $6 > x \geq 3$

Find the sum or difference. Write the answer in standard form. - $i \sqrt { 7 } + 9 - ( 4 + 7 i \sqrt { 7 } ) - ( 9 - i \sqrt { 7 } )$

Decide what values of the variable cannot possibly be solutions for the equation. - $( 10 + x ) ^ { 1 / 2 } + ( 11 - 5 x ) ^ { 1 / 2 } = - 1$

Solve the equation by completing the square. - $8 x ^ { 2 } + 7 x = - 2$

Solve and graph the inequality. Give answer in interval notation. - $\frac { x - 2 } { 18 } \geq \frac { x - 5 } { 24 } + \frac { 1 } { 72 }$ $Solve and graph the inequality. Give answer in interval notation. - \frac { x - 2 } { 18 } \geq \frac { x - 5 } { 24 } + \frac { 1 } { 72 }$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } + 8 x + 12 \geq 0$

Solve the problem -Find two consecutive odd integers whose product is 483.

Write the statement as an absolute value inequality. -In a milling operation, the thickness of the wood panels that can be produced satisfies the inequality $| \mathrm { x } - 1.88 | \leq 1.20$ . What range of thicknesses corresponds to this inequality?

Solve the problem. -A triangular shaped lake-front lot has a perimeter of 1200 ft. One side is 100 ft longer than the shortest side, while the third side is 200 ft longer than the shortest side. Find the lengths of all three Sides.

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } + 3 x + 2 > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 7 } { x - 4 } = 1 + \frac { 9 } { x + 4 }$

Solve for the indicated variable. - $\mathrm { Ve } = \frac { 1 } { 2 } \mathrm { mv } ^ { 2 }$ , for $\mathrm { v }$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } - 3 x \leq - 2$

Determine whether or not the equation is linear. - $6 x ^ { 2 } - 5 x + 9 = 0$

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| < 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 5 } { x - 1 } - \frac { 8 x } { 1 - x } = 10$

Find the quotient. Write the answer in standard form. - $\frac { 10 } { - i }$

Solve the equation. - $\left| 9 x ^ { 3 } + 3 x ^ { 2 } - 6 x \right| = 0$

Solve the equation by completing the square. - $x ^ { 2 } + 4 x + 8 = 0$

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

Decide what values of the variable cannot possibly be solutions for the equation. - x4+720=89x2x ^ { 4 } + 720 = 89 x ^ { 2 }x4+720=89x2

Write the inequality in interval notation. - 6>x≥36 > x \geq 36>x≥3

Find the sum or difference. Write the answer in standard form. - i7+9−(4+7i7)−(9−i7)i \sqrt { 7 } + 9 - ( 4 + 7 i \sqrt { 7 } ) - ( 9 - i \sqrt { 7 } )i7​+9−(4+7i7​)−(9−i7​)

Decide what values of the variable cannot possibly be solutions for the equation. - (10+x)1/2+(11−5x)1/2=−1( 10 + x ) ^ { 1 / 2 } + ( 11 - 5 x ) ^ { 1 / 2 } = - 1(10+x)1/2+(11−5x)1/2=−1

Solve the equation by completing the square. - 8x2+7x=−28 x ^ { 2 } + 7 x = - 28x2+7x=−2

Solve and graph the inequality. Give answer in interval notation. - x−218≥x−524+172\frac { x - 2 } { 18 } \geq \frac { x - 5 } { 24 } + \frac { 1 } { 72 }18x−2​≥24x−5​+721​

Solve the quadratic inequality. Write the solution set in interval notation. - x2+8x+12≥0x ^ { 2 } + 8 x + 12 \geq 0x2+8x+12≥0