Question 1

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { - 5 x + 6 } { 3 x ^ { 2 } + 2 } > 0$$

Accepted Answer

A)  $\left( - \infty , \frac { 6 } { 5 } \right)$ 
B)  $\left( - \frac { 6 } { 5 } , \infty \right)$ 
C)  $( - \infty , 0 )$ 
D)  $\left( - \infty , - \frac { 5 } { 6 } \right)$ 
A)  $\left( - \infty , \frac { 6 } { 5 } \right)$ 
B)  $\left( - \frac { 6 } { 5 } , \infty \right)$ 
C)  $( - \infty , 0 )$ 
D)  $\left( - \infty , - \frac { 5 } { 6 } \right)$ A

Question 2

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { x } { x - 5 } - \frac { 1 } { x + 9 } = \frac { 11 } { x ^ { 2 } + 4 x - 45 }$$

Accepted Answer

A)  $- 5,0,9$ 
B)  $- 9,5$ 
C)  $- 9,0,5$ 
D)  $- 5,9 , - 45$ 
A)  $- 5,0,9$ 
B)  $- 9,5$ 
C)  $- 9,0,5$ 
D)  $- 5,9 , - 45$ B

Question 3

Solve and graph the inequality. Give answer in interval notation.
-$$\frac { x - 1 } { 20 } \geq \frac { x - 5 } { 24 } + \frac { 1 } { 120 }$$

Accepted Answer

A)  $[ - 18 , \infty )$
  
B)  $( - \infty , - 18 )$
  
C)  $( - 18 , \infty )$
  
D)  $( - \infty , - 18 ]$
  
A)  $[ - 18 , \infty )$
  
B)  $( - \infty , - 18 )$
  
C)  $( - 18 , \infty )$
  
D)  $( - \infty , - 18 ]$
  A

Question 4

Solve the equation.
-$$\left| \frac { 3 x + 2 } { 8 x - 5 } \right| = 8$$

Accepted Answer

A)  $\left\{ 2 , - \frac { 10 } { 3 } \right\}$ 
B)  $\left\{ \frac { 42 } { 61 } , \frac { 38 } { 67 } \right\}$ 
C)  $\left\{ \frac { 38 } { 61 } , \frac { 42 } { 67 } \right\}$ 
D)  $\left\{ - \frac { 42 } { 67 } , \frac { 10 } { 61 } \right\}$ 
A)  $\left\{ 2 , - \frac { 10 } { 3 } \right\}$ 
B)  $\left\{ \frac { 42 } { 61 } , \frac { 38 } { 67 } \right\}$ 
C)  $\left\{ \frac { 38 } { 61 } , \frac { 42 } { 67 } \right\}$ 
D)  $\left\{ - \frac { 42 } { 67 } , \frac { 10 } { 61 } \right\}$

Question 5

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 1 } { x - 4 } - \frac { 1 } { x + 8 } = 10$$

Accepted Answer

A)  $- \frac { 1 } { 4 } , \frac { 1 } { 8 }$ 
B)  $- 8,4$ 
C)  $- 4,8$ 
D)  $- \frac { 1 } { 8 } , \frac { 1 } { 4 }$ 
A)  $- \frac { 1 } { 4 } , \frac { 1 } { 8 }$ 
B)  $- 8,4$ 
C)  $- 4,8$ 
D)  $- \frac { 1 } { 8 } , \frac { 1 } { 4 }$

Question 6

Solve and graph the inequality. Give answer in interval notation.
-$$- 6 ( 6 x + 5 ) < - 42 x + 12$$

Accepted Answer

A)  $( - \infty , - 42 )$
  
B)  $( - 42 , \infty )$
  
C)  $( - \infty , 7 )$
  
D)  $( 7 , \infty )$
  
A)  $( - \infty , - 42 )$
  
B)  $( - 42 , \infty )$
  
C)  $( - \infty , 7 )$
  
D)  $( 7 , \infty )$

Question 7

Determine whether or not the equation is linear.
-$$3 x ^ { 2 } - 7 x + 2 = 0$$

Accepted Answer

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

Question 8

Solve the inequality. Write the solution set in interval notation.
-$5 + \left| 1 - \frac { 1 } { 2 } x \right| \geq 8$

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Solve the formula for the indicated variable.
-$\mathrm { P } = \mathrm { s } _ { 1 } + \mathrm { s } _ { 2 } + \mathrm { s } _ { 3 }$, for $\mathrm { s } _ { 1 }$

Accepted Answer

A)  $s _ { 1 } = s _ { 2 } + s _ { 3 } - P$ 
B)  $s _ { 1 } = P + s _ { 2 } + s _ { 3 }$ 
C)  $s _ { 1 } = s _ { 2 } + P - s _ { 3 }$ 
D)  $s _ { 1 } = P - s _ { 2 } - s _ { 3 }$ 
A)  $s _ { 1 } = s _ { 2 } + s _ { 3 } - P$ 
B)  $s _ { 1 } = P + s _ { 2 } + s _ { 3 }$ 
C)  $s _ { 1 } = s _ { 2 } + P - s _ { 3 }$ 
D)  $s _ { 1 } = P - s _ { 2 } - s _ { 3 }$

Question 11

Solve the problem.
-How many liters of a 30% alcohol solution must be mixed with 50 liters of a 70% solution to get a 40% solution?

Accepted Answer

A)  20 L 
B) 15 L 
C)  150 L 
D)  200 L 
A)  20 L 
B) 15 L 
C)  150 L 
D)  200 L

Question 12

Solve the inequality. Write the solution set in interval notation.
-$$\left| x ^ { 4 } + 12 x ^ { 2 } + 36 \right| < 0$$

Accepted Answer

A)  $\varnothing$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 6 ) \cup ( 6 , \infty )$ 
D)  $( - 6,6 )$ 
A)  $\varnothing$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 6 ) \cup ( 6 , \infty )$ 
D)  $( - 6,6 )$

Question 13

Solve the inequality. Write the solution set in interval notation.
-$$| x + 9 | < 0$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 9 \}$ 
C)  $\{ - 9 \}$ 
D)  $( - \infty , - 9 )$ 
A)  $\varnothing$ 
B)  $\{ 9 \}$ 
C)  $\{ - 9 \}$ 
D)  $( - \infty , - 9 )$

Question 14

Find the quotient. Write the answer in standard form.
-$$\frac { 2 - 5 i } { 5 - 6 i }$$

Accepted Answer

A)  $- \frac { 20 } { 61 } + \frac { 37 } { 61 } \mathrm { i }$ 
B)  $- \frac { 40 } { 11 } - \frac { 13 } { 11 } \mathrm { i }$ 
C)  $\frac { 40 } { 61 } - \frac { 13 } { 61 } \mathrm { i }$ 
D)  $\frac { 20 } { 11 } - \frac { 13 } { 11 } \mathrm { i }$ 
A)  $- \frac { 20 } { 61 } + \frac { 37 } { 61 } \mathrm { i }$ 
B)  $- \frac { 40 } { 11 } - \frac { 13 } { 11 } \mathrm { i }$ 
C)  $\frac { 40 } { 61 } - \frac { 13 } { 61 } \mathrm { i }$ 
D)  $\frac { 20 } { 11 } - \frac { 13 } { 11 } \mathrm { i }$

Question 15

Simplify the power of i.
-$\frac { 1 } { i ^ { - 12 } }$

Accepted Answer

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

Question 16

Solve and graph the inequality. Give answer in interval notation.
-$$- 2 x - 9 > - 3 x - 8$$

Accepted Answer

A)  $( - \infty , - 17 )$
  
B)  $( - 17 , \infty )$
  
C)  $( - \infty , 1 )$
  
D)  $( 1 , \infty )$
  
A)  $( - \infty , - 17 )$
  
B)  $( - 17 , \infty )$
  
C)  $( - \infty , 1 )$
  
D)  $( 1 , \infty )$

Question 17

Determine whether or not the equation is linear.
-6x = 7x + 8x

Accepted Answer

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

Question 18

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } ( x + 81 ) ^ { 2 } \geq 0$$

Accepted Answer

A)  $( - \infty , - 9 ] \cup [ 0,9 ]$ 
B)  $\varnothing$ 
C)  $[ - 9,0 ] \cup [ 9 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $( - \infty , - 9 ] \cup [ 0,9 ]$ 
B)  $\varnothing$ 
C)  $[ - 9,0 ] \cup [ 9 , \infty )$ 
D)  $( - \infty , \infty )$

Question 19

Solve the inequality. Write the solution set in interval notation.
-$$| x + 2 | > 9$$

Accepted Answer

A)  $( 7 , \infty )$ 
B)  $( - \infty , - 11 ) \cup ( 7 , \infty )$ 
C)  $\varnothing$ 
D)  $( - 11,7 )$ 
A)  $( 7 , \infty )$ 
B)  $( - \infty , - 11 ) \cup ( 7 , \infty )$ 
C)  $\varnothing$ 
D)  $( - 11,7 )$

Question 20

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { x + 8 } { x + 7 } < 2$$

Accepted Answer

A)  $\varnothing$ 
B)  $( - \infty , - 7 ) \cup ( - 6 , \infty )$ 
C)  $( - \infty , - 6 ) \cup ( 7 , \infty )$ 
D)  $( - 7 , - 6 )$ 
A)  $\varnothing$ 
B)  $( - \infty , - 7 ) \cup ( - 6 , \infty )$ 
C)  $( - \infty , - 6 ) \cup ( 7 , \infty )$ 
D)  $( - 7 , - 6 )$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { - 5 x + 6 } { 3 x ^ { 2 } + 2 } > 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { x } { x - 5 } - \frac { 1 } { x + 9 } = \frac { 11 } { x ^ { 2 } + 4 x - 45 }$

Solve and graph the inequality. Give answer in interval notation. - $\frac { x - 1 } { 20 } \geq \frac { x - 5 } { 24 } + \frac { 1 } { 120 }$ $Solve and graph the inequality. Give answer in interval notation. - \frac { x - 1 } { 20 } \geq \frac { x - 5 } { 24 } + \frac { 1 } { 120 }$

Solve the equation. - $\left| \frac { 3 x + 2 } { 8 x - 5 } \right| = 8$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { x - 4 } - \frac { 1 } { x + 8 } = 10$

Solve and graph the inequality. Give answer in interval notation. - $- 6 ( 6 x + 5 ) < - 42 x + 12$

Determine whether or not the equation is linear. - $3 x ^ { 2 } - 7 x + 2 = 0$

Solve the inequality. Write the solution set in interval notation. - $5 + \left| 1 - \frac { 1 } { 2 } x \right| \geq 8$

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

Solve the formula for the indicated variable. - $\mathrm { P } = \mathrm { s } _ { 1 } + \mathrm { s } _ { 2 } + \mathrm { s } _ { 3 }$ , for $\mathrm { s } _ { 1 }$

Solve the problem. -How many liters of a 30% alcohol solution must be mixed with 50 liters of a 70% solution to get a 40% solution?

Solve the inequality. Write the solution set in interval notation. - $\left| x ^ { 4 } + 12 x ^ { 2 } + 36 \right| < 0$

Solve the inequality. Write the solution set in interval notation. - $| x + 9 | < 0$

Find the quotient. Write the answer in standard form. - $\frac { 2 - 5 i } { 5 - 6 i }$

Simplify the power of i. - $\frac { 1 } { i ^ { - 12 } }$

Solve and graph the inequality. Give answer in interval notation. - $- 2 x - 9 > - 3 x - 8$

Determine whether or not the equation is linear. -6x = 7x + 8x

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } ( x + 81 ) ^ { 2 } \geq 0$

Solve the inequality. Write the solution set in interval notation. - $| x + 2 | > 9$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { x + 8 } { x + 7 } < 2$

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 rational inequality. Write the solution set in interval notation. - −5x+63x2+2>0\frac { - 5 x + 6 } { 3 x ^ { 2 } + 2 } > 03x2+2−5x+6​>0

Decide what values of the variable cannot possibly be solutions for the equation. - xx−5−1x+9=11x2+4x−45\frac { x } { x - 5 } - \frac { 1 } { x + 9 } = \frac { 11 } { x ^ { 2 } + 4 x - 45 }x−5x​−x+91​=x2+4x−4511​

Solve and graph the inequality. Give answer in interval notation. - x−120≥x−524+1120\frac { x - 1 } { 20 } \geq \frac { x - 5 } { 24 } + \frac { 1 } { 120 }20x−1​≥24x−5​+1201​

Solve the equation. - ∣3x+28x−5∣=8\left| \frac { 3 x + 2 } { 8 x - 5 } \right| = 8​8x−53x+2​​=8

Decide what values of the variable cannot possibly be solutions for the equation. - 1x−4−1x+8=10\frac { 1 } { x - 4 } - \frac { 1 } { x + 8 } = 10x−41​−x+81​=10

Solve and graph the inequality. Give answer in interval notation. - −6(6x+5)<−42x+12- 6 ( 6 x + 5 ) < - 42 x + 12−6(6x+5)<−42x+12

Determine whether or not the equation is linear. - 3x2−7x+2=03 x ^ { 2 } - 7 x + 2 = 03x2−7x+2=0

Solve the inequality. Write the solution set in interval notation. - 5+∣1−12x∣≥85 + \left| 1 - \frac { 1 } { 2 } x \right| \geq 85+​1−21​x​≥8

Write the inequality in interval notation. - −3≤x<3- 3 \leq x < 3−3≤x<3

Solve the formula for the indicated variable. - P=s1+s2+s3\mathrm { P } = \mathrm { s } _ { 1 } + \mathrm { s } _ { 2 } + \mathrm { s } _ { 3 }P=s1​+s2​+s3​ , for s1\mathrm { s } _ { 1 }s1​