Question 1

Solve and graph the inequality. Give answer in interval notation.
-$$13 x - 4 > 12 x + 1$$

Accepted Answer

A)  $( - \infty , 5 )$
  
B)  $( 5 , \infty )$
  
C)  $( - 3 , \infty )$
  
D)  $( - \infty , - 3 )$
  
A)  $( - \infty , 5 )$
  
B)  $( 5 , \infty )$
  
C)  $( - 3 , \infty )$
  
D)  $( - \infty , - 3 )$

Question 2

Solve for y.
-$$y - 4 ( x + 10 ) = 2 + 2 y$$

Accepted Answer

A)  $y = 4 x + 42$ 
B)  $y = 4 x + 38$ 
C)  $y = - 4 x - 42$ 
D)  $y = - 4 x + 42$ 
A)  $y = 4 x + 42$ 
B)  $y = 4 x + 38$ 
C)  $y = - 4 x - 42$ 
D)  $y = - 4 x + 42$

Question 3

Solve the formula for the indicated variable.
-$\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } )$, for $\mathrm { r }$

Accepted Answer

A)  $r = \frac { A - P } { P n }$ 
B)  $r = \frac { P n } { A - P }$ 
C)  $r = \frac { P - A } { P n }$ 
D)  $r = \frac { A } { n }$ 
A)  $r = \frac { A - P } { P n }$ 
B)  $r = \frac { P n } { A - P }$ 
C)  $r = \frac { P - A } { P n }$ 
D)  $r = \frac { A } { n }$

Question 4

Answer the question
-To solve for the lengths of the right triangle sides, which equation is correct?

Accepted Answer

A)  $( 2 x - 10 ) ^ { 2 } = x ^ { 2 } + ( 3 x ) ^ { 2 }$ 
B)  $x ^ { 2 } = ( 3 x ) ^ { 2 } + ( 2 x - 10 ) ^ { 2 }$ 
C)  $( 2 x - 10 ) ^ { 2 } + x ^ { 2 } = ( 3 x ) ^ { 2 }$ 
D)  $x ^ { 2 } + ( 3 x ) ^ { 2 } = ( 2 x - 10 ) ^ { 2 }$ 
A)  $( 2 x - 10 ) ^ { 2 } = x ^ { 2 } + ( 3 x ) ^ { 2 }$ 
B)  $x ^ { 2 } = ( 3 x ) ^ { 2 } + ( 2 x - 10 ) ^ { 2 }$ 
C)  $( 2 x - 10 ) ^ { 2 } + x ^ { 2 } = ( 3 x ) ^ { 2 }$ 
D)  $x ^ { 2 } + ( 3 x ) ^ { 2 } = ( 2 x - 10 ) ^ { 2 }$

Question 5

Solve the inequality. Write the solution set in interval notation.
-$$| 2 - 3 x | \geq 11$$

Accepted Answer

A)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
B)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
C)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right]$ 
D)  $\left[ - 3 , \frac { 13 } { 3 } \right]$ 
A)  $( - \infty , - 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right)$ 
B)  $\left[ - \frac { 13 } { 3 } , 3 \right]$ 
C)  $( - \infty , 3 ] \cup \left[ \frac { 13 } { 3 } , \infty \right]$ 
D)  $\left[ - 3 , \frac { 13 } { 3 } \right]$

Question 6

Solve the equation.
-$$x - 19 = 0$$

Accepted Answer

A)  19 
B)  $\pm 19$ 
C)  $- 19$ 
D)  $\sqrt { 19 }$ 
A)  19 
B)  $\pm 19$ 
C)  $- 19$ 
D)  $\sqrt { 19 }$

Question 7

Write the statement as an absolute value inequality.
-$\mathrm { z }$ is no less than 7 units from 12

Accepted Answer

A)  $| z - 12 | \leq 7$ 
B)  $| z - 7 | > 12$ 
C)  $| z - 12 | \geq 7$ 
D)  $| z - 12 | > 7$ 
A)  $| z - 12 | \leq 7$ 
B)  $| z - 7 | > 12$ 
C)  $| z - 12 | \geq 7$ 
D)  $| z - 12 | > 7$

Question 8

Solve the equation.
-$$| x - 7 | + 3 = 6$$

Accepted Answer

A)  $\{ 10,4 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ - 10 , - 4 \}$ 
D)  $\varnothing$ 
A)  $\{ 10,4 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ - 10 , - 4 \}$ 
D)  $\varnothing$

Question 9

Solve the problem.
-A 15 in by 25 in rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 551 in2?

Accepted Answer

A)  3 in 
B)  1 in 
C)  3.5 in 
D)  2 in 
A)  3 in 
B)  1 in 
C)  3.5 in 
D)  2 in

Question 10

Solve and graph the inequality. Give answer in interval notation.
-$$2 x + 1 \geq 3 x - 7$$

Accepted Answer

A)  $( - \infty , 8 ]$
  
B)  $( 2 , \infty )$
  
C)  $[ - 8 , \infty )$
  
D)  $( - \infty , 2 ]$
 
\ 
A)  $( - \infty , 8 ]$
  
B)  $( 2 , \infty )$
  
C)  $[ - 8 , \infty )$
  
D)  $( - \infty , 2 ]$
 
\

Question 11

Solve the quadratic inequality. Write the solution set in interval notation.
-$$x ^ { 2 } + 18 x + 76 \geq 0$$

Accepted Answer

A)  $[ - 9 - \sqrt { 5 } , - 9 + \sqrt { 5 } ]$ 
B)  $( - \infty , - 9 - \sqrt { 5 } ] \cup [ - 9 + \sqrt { 5 } , \infty )$ 
C)  $( - \infty , - 9 - \sqrt { 5 } ) \cup ( - 9 + \sqrt { 5 } , \infty )$ 
D)  $( - \infty , - \sqrt { 5 } ] \cup [ \sqrt { 5 } , \infty )$ 
A)  $[ - 9 - \sqrt { 5 } , - 9 + \sqrt { 5 } ]$ 
B)  $( - \infty , - 9 - \sqrt { 5 } ] \cup [ - 9 + \sqrt { 5 } , \infty )$ 
C)  $( - \infty , - 9 - \sqrt { 5 } ) \cup ( - 9 + \sqrt { 5 } , \infty )$ 
D)  $( - \infty , - \sqrt { 5 } ] \cup [ \sqrt { 5 } , \infty )$

Question 12

Solve for y.
-$$8 y + x ^ { 2 } = x + 10$$

Accepted Answer

A)  $y = x + 10 - x ^ { 2 }$ 
B)  $y = \frac { x + 10 - x ^ { 2 } } { 8 }$ 
C)  $y = \frac { x ^ { 2 } - x - 10 } { 8 }$ 
D)  $y = x ^ { 2 } - x - 10$ 
A)  $y = x + 10 - x ^ { 2 }$ 
B)  $y = \frac { x + 10 - x ^ { 2 } } { 8 }$ 
C)  $y = \frac { x ^ { 2 } - x - 10 } { 8 }$ 
D)  $y = x ^ { 2 } - x - 10$

Question 13

Find the quotient. Write the answer in standard form.
-$$\frac { 8 - 7 i } { 5 + 4 i }$$

Accepted Answer

A)  $\frac { 4 } { 3 } + \frac { 67 } { 9 } \mathrm { i }$ 
B)  $\frac { 12 } { 41 } - \frac { 67 } { 41 } i$ 
C)  $\frac { 68 } { 41 } + \frac { 3 } { 41 } i$ 
D)  $\frac { 68 } { 9 } + \frac { 67 } { 9 } \mathrm { i }$ 
A)  $\frac { 4 } { 3 } + \frac { 67 } { 9 } \mathrm { i }$ 
B)  $\frac { 12 } { 41 } - \frac { 67 } { 41 } i$ 
C)  $\frac { 68 } { 41 } + \frac { 3 } { 41 } i$ 
D)  $\frac { 68 } { 9 } + \frac { 67 } { 9 } \mathrm { i }$

Question 14

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } - 1 = 0$$

Accepted Answer

A)  $\left\{ 1 , - \frac { 1 } { 2 } \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$ 
B)  $\{ 1 , - 1 \pm i \sqrt { 3 } \}$ 
C)  $\{ 1,1 \pm i \sqrt { 3 } \}$ 
D)  $\{ 1 , \pm i \}$ 
A)  $\left\{ 1 , - \frac { 1 } { 2 } \pm \frac { \sqrt { 3 } } { 2 } \mathrm { i } \right\}$ 
B)  $\{ 1 , - 1 \pm i \sqrt { 3 } \}$ 
C)  $\{ 1,1 \pm i \sqrt { 3 } \}$ 
D)  $\{ 1 , \pm i \}$

Question 15

Write the number as the product of a real number and i.
-$- \sqrt { - 25 }$

Accepted Answer

A)  i $\sqrt { 25 }$ 
B)  $- 5 \mathrm { i }$ 
C)  5 
D)  $5 \mathrm { i }$ 
A)  i $\sqrt { 25 }$ 
B)  $- 5 \mathrm { i }$ 
C)  5 
D)  $5 \mathrm { i }$

Question 16

Solve the quadratic inequality. Write the solution set in interval notation.
-$$- 3 x ^ { 2 } + 3 x - 5 \leq 0$$

Accepted Answer

A)  $\left[ \frac { 1 } { 3 } , 5 \right]$ 
B)  $\left[ - 3 , - \frac { 1 } { 5 } \right]$ 
C)  $\varnothing$ 
D)  $( - \infty , \infty )$ 
A)  $\left[ \frac { 1 } { 3 } , 5 \right]$ 
B)  $\left[ - 3 , - \frac { 1 } { 5 } \right]$ 
C)  $\varnothing$ 
D)  $( - \infty , \infty )$

Question 17

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$$8 + \sqrt { 11 } , 8 - \sqrt { 11 }$$

Accepted Answer

A)  $x ^ { 2 } + 16 x + 53 = 0$ 
B)  $x ^ { 2 } + 64 x + 75 = 0$ 
C)  $x ^ { 2 } - 16 x + 53 = 0$ 
D)  $x ^ { 2 } - 16 x + 75 = 0$ 
A)  $x ^ { 2 } + 16 x + 53 = 0$ 
B)  $x ^ { 2 } + 64 x + 75 = 0$ 
C)  $x ^ { 2 } - 16 x + 53 = 0$ 
D)  $x ^ { 2 } - 16 x + 75 = 0$

Question 18

Solve the equation.
-$$| 3 - 2 x | = 4$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 2 } , \frac { 7 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 2 } , \frac { 1 } { 2 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 2 } , \frac { 7 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , - \frac { 1 } { 2 } \right\}$ 
D)  $\left\{ - \frac { 7 } { 2 } , \frac { 1 } { 2 } \right\}$

Question 19

Solve the quadratic inequality. Write the solution set in interval notation.
-$$( 5 - 4 x ) ^ { 2 } \geq - 25$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left( - \infty , \frac { 5 } { 2 } \right) \cup ( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $\left[ \frac { 5 } { 2 } , 0 \right]$ 
A)  $\varnothing$ 
B)  $\left( - \infty , \frac { 5 } { 2 } \right) \cup ( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $\left[ \frac { 5 } { 2 } , 0 \right]$

Question 20

Determine whether or not the equation is linear.
-6x - 5 = 0

Accepted Answer

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

Solve and graph the inequality. Give answer in interval notation. - $13 x - 4 > 12 x + 1$

Solve for y. - $y - 4 ( x + 10 ) = 2 + 2 y$

Solve the formula for the indicated variable. - $\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } )$ , for $\mathrm { r }$

Answer the question -To solve for the lengths of the right triangle sides, which equation is correct?

Solve the inequality. Write the solution set in interval notation. - $| 2 - 3 x | \geq 11$

Solve the equation. - $x - 19 = 0$

Write the statement as an absolute value inequality. - $\mathrm { z }$ is no less than 7 units from 12

Solve the equation. - $| x - 7 | + 3 = 6$

Solve the problem. -A 15 in by 25 in rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 551 in2?

Solve and graph the inequality. Give answer in interval notation. - $2 x + 1 \geq 3 x - 7$ $Solve and graph the inequality. Give answer in interval notation. - 2 x + 1 \geq 3 x - 7$

Solve the quadratic inequality. Write the solution set in interval notation. - $x ^ { 2 } + 18 x + 76 \geq 0$

Solve for y. - $8 y + x ^ { 2 } = x + 10$

Find the quotient. Write the answer in standard form. - $\frac { 8 - 7 i } { 5 + 4 i }$

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } - 1 = 0$

Write the number as the product of a real number and i. - $- \sqrt { - 25 }$

Solve the quadratic inequality. Write the solution set in interval notation. - $- 3 x ^ { 2 } + 3 x - 5 \leq 0$

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $8 + \sqrt { 11 } , 8 - \sqrt { 11 }$

Solve the equation. - $| 3 - 2 x | = 4$

Solve the quadratic inequality. Write the solution set in interval notation. - $( 5 - 4 x ) ^ { 2 } \geq - 25$

Determine whether or not the equation is linear. -6x - 5 = 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

Solve and graph the inequality. Give answer in interval notation. - 13x−4>12x+113 x - 4 > 12 x + 113x−4>12x+1

Solve for y. - y−4(x+10)=2+2yy - 4 ( x + 10 ) = 2 + 2 yy−4(x+10)=2+2y

Solve the formula for the indicated variable. - A=P(1+nr)\mathrm { A } = \mathrm { P } ( 1 + \mathrm { nr } )A=P(1+nr) , for r\mathrm { r }r

Answer the question -To solve for the lengths of the right triangle sides, which equation is correct?

Solve the inequality. Write the solution set in interval notation. - ∣2−3x∣≥11| 2 - 3 x | \geq 11∣2−3x∣≥11

Solve the equation. - x−19=0x - 19 = 0x−19=0

Write the statement as an absolute value inequality. - z\mathrm { z }z is no less than 7 units from 12

Solve the equation. - ∣x−7∣+3=6| x - 7 | + 3 = 6∣x−7∣+3=6