Question 1

Graph the solution set.
-$$| 2 x + 5 | + 8 = 14$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } , - \frac { 11 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 2 } , \frac { 11 } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 } { 5 } , - \frac { 11 } { 5 } \right\}$ 
D)  $\varnothing$ 
A)  $\left\{ \frac { 1 } { 2 } , - \frac { 11 } { 2 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 2 } , \frac { 11 } { 2 } \right\}$ 
C)  $\left\{ \frac { 1 } { 5 } , - \frac { 11 } { 5 } \right\}$ 
D)  $\varnothing$

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$| - 3 x - 9 | \geq - 3$$

Accepted Answer

A)  $\varnothing$ 
B)  $( - \infty , - 2 )$ 
C)  $( - \infty , \infty )$ 
D)  $( - 4 , - 2 )$ 
A)  $\varnothing$ 
B)  $( - \infty , - 2 )$ 
C)  $( - \infty , \infty )$ 
D)  $( - 4 , - 2 )$

Question 3

Solve and graph the inequality. Give answer in interval notation.
-$$8 + 6 x + 2 \geq 5 x + 7$$

Accepted Answer

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

Question 4

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { 1 } { x - 5 } > 0$$

Accepted Answer

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

Question 5

Determine whether or not the equation is linear.
-$$- 7.9 x + 1.2 = - 67.8 - 1.0 x$$

Accepted Answer

A)  $\{ 8.7 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ 8.9 \}$ 
D)  $\{ - 76 \}$ 
A)  $\{ 8.7 \}$ 
B)  $\{ 10 \}$ 
C)  $\{ 8.9 \}$ 
D)  $\{ - 76 \}$

Question 6

The profit made when $t$ units are sold, $t > 0$, is given by $P = t ^ { 2 } - 27 t + 176$. Determine the number of units to be sold in order for $\mathrm { P } < 0$ (a loss is taken).

Accepted Answer

A)  $11  0$ 
C)  $t = 11$ or $t = 16$ 
D)  $t  16$ 
A)  $11  0$ 
C)  $t = 11$ or $t = 16$ 
D)  $t  16$

Question 7

The number of non-text books read by college students ranges from 6 to 44 . Using B as the variable, write an absolute value inequality that corresponds to this range.

Accepted Answer

A)  $| B - 38 | \leq 6$ 
B)  $| \mathrm { B } - 19 | \leq 25$ 
C)  $| B - 6 | \leq 38$ 
D)  $| B - 25 | \leq 19$ 
A)  $| B - 38 | \leq 6$ 
B)  $| \mathrm { B } - 19 | \leq 25$ 
C)  $| B - 6 | \leq 38$ 
D)  $| B - 25 | \leq 19$

Question 8

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

Accepted Answer

A)  $\left( - \infty , - \frac { 25 } { 3 } \right]$
  
B)  $\left( - \infty , - \frac { 25 } { 3 } \right)$
  
C)  $\left( - \frac { 25 } { 3 } , \infty \right)$
  
D)  $\left[ - \frac { 25 } { 3 } , \infty \right]$
  
A)  $\left( - \infty , - \frac { 25 } { 3 } \right]$
  
B)  $\left( - \infty , - \frac { 25 } { 3 } \right)$
  
C)  $\left( - \frac { 25 } { 3 } , \infty \right)$
  
D)  $\left[ - \frac { 25 } { 3 } , \infty \right]$

Question 9

Solve the problem.
-Walt made an extra $10,000 last year from a part-time job. He invested part of the money at 2% and the rest at 3.25%. He made a total of $237.50 in interest. How much was invested at 3.25%?

Accepted Answer

A)  $5000 
B)  $8000 
C)  $7000 
D)  $3000 
A)  $5000 
B)  $8000 
C)  $7000 
D)  $3000

Question 10

The position of an object moving in a straight line is given by s $s = 2 t ^ { 2 } - 3 t$ 3t, 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 9
Meters?

Accepted Answer

A)  10.0 sec 
B)  3.0 sec 
C)  2.8 sec 
D)  13.5 sec 
A)  10.0 sec 
B)  3.0 sec 
C)  2.8 sec 
D)  13.5 sec

Question 11

Decide what values of the variable cannot possibly be solutions for the equation.
-$$1 - \frac { 7 } { x } - \frac { 18 } { x ^ { 2 } } = 0$$

Accepted Answer

A)  $\{ 9,2 \}$ 
B)  $\{ - 9,2 \}$ 
C)  $\{ 9 , - 2 \}$ 
D)  $\{ - 9 , - 2 \}$ 
A)  $\{ 9,2 \}$ 
B)  $\{ - 9,2 \}$ 
C)  $\{ 9 , - 2 \}$ 
D)  $\{ - 9 , - 2 \}$

Question 12

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$2 , - 9$

Accepted Answer

A)  $x ^ { 2 } + 7 x - 18 = 0$ 
B)  $x ^ { 2 } - 18 x + 7 = 0$ 
C)  $x ^ { 2 } - 7 x - 18 = 0$ 
D)  $x ^ { 2 } - 18 x - 7 = 0$ 
A)  $x ^ { 2 } + 7 x - 18 = 0$ 
B)  $x ^ { 2 } - 18 x + 7 = 0$ 
C)  $x ^ { 2 } - 7 x - 18 = 0$ 
D)  $x ^ { 2 } - 18 x - 7 = 0$

Question 13

Solve the equation by the square root property.
-$$x ^ { 2 } = 20$$

Accepted Answer

A)  $\{ 400 \}$ 
B)  $\{ \pm 2 \sqrt { 5 } \}$ 
C)  $\{ 10 \}$ 
D)  $\{ \sqrt { 20 } \}$ 
A)  $\{ 400 \}$ 
B)  $\{ \pm 2 \sqrt { 5 } \}$ 
C)  $\{ 10 \}$ 
D)  $\{ \sqrt { 20 } \}$

Question 14

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 4 } { x - 1 } + \frac { 6 x } { 1 - x } = 11$$

Accepted Answer

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

Question 15

Graph the solution set.
-$$| x - 5 | = 0$$

Accepted Answer

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

Question 16

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 3 } + 4 x ^ { 2 } - 9 x - 36 \geq 0$$

Accepted Answer

A)  $[ - 4 , \infty )$ 
B)  $[ - 4 , - 3 ] \cup [ 3 , \infty )$ 
C)  $[ - 3,3 ] \cup [ 4 , \infty )$ 
D)  $[ - 4,3 ]$ 
A)  $[ - 4 , \infty )$ 
B)  $[ - 4 , - 3 ] \cup [ 3 , \infty )$ 
C)  $[ - 3,3 ] \cup [ 4 , \infty )$ 
D)  $[ - 4,3 ]$

Question 17

Graph the solution set.
-$$| 7 x + 6 | = | 1 - 10 x |$$

Accepted Answer

A)  $\left\{ - \frac { 7 } { 17 } , 1 \right\}$ 
B)  $\left\{ \frac { 7 } { 17 } , 1 \right\}$ 
C)  $\left\{ - \frac { 5 } { 17 } , \frac { 7 } { 3 } \right\}$ 
D)  $\left\{ \frac { 5 } { 3 } , - \frac { 7 } { 17 } \right\}$ 
A)  $\left\{ - \frac { 7 } { 17 } , 1 \right\}$ 
B)  $\left\{ \frac { 7 } { 17 } , 1 \right\}$ 
C)  $\left\{ - \frac { 5 } { 17 } , \frac { 7 } { 3 } \right\}$ 
D)  $\left\{ \frac { 5 } { 3 } , - \frac { 7 } { 17 } \right\}$

Question 18

Solve the inequality. Write the solution set in interval notation.
-$$\left| \frac { 5 } { 6 } - \frac { 1 } { 7 } x \right| > \frac { 2 } { 9 }$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , - \frac { 133 } { 18 } \right) \cup \left( \frac { 77 } { 18 } , \infty \right)$ 
C)  $\left( \frac { 77 } { 18 } , \frac { 133 } { 18 } \right)$ 
D)  $\left( - \infty , \frac { 77 } { 18 } \right) \cup \left( \frac { 133 } { 18 } , \infty \right)$ 
A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , - \frac { 133 } { 18 } \right) \cup \left( \frac { 77 } { 18 } , \infty \right)$ 
C)  $\left( \frac { 77 } { 18 } , \frac { 133 } { 18 } \right)$ 
D)  $\left( - \infty , \frac { 77 } { 18 } \right) \cup \left( \frac { 133 } { 18 } , \infty \right)$

Question 19

Solve and graph the inequality. Give answer in interval notation.
-$$\frac { x - 2 } { 24 } \geq \frac { x - 2 } { 30 } + \frac { 1 } { 120 }$$

Accepted Answer

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

Question 20

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then
use those values to write a quadratic equation.
-$24 \mathrm { i } , - 24 \mathrm { i }$

Accepted Answer

A)  $x ^ { 2 } + 576 = 0$ 
B)  $x ^ { 2 } + 48 + 576 = 0$ 
C)  $x ^ { 2 } - 48 - 576 = 0$ 
D)  $x ^ { 2 } - 576 = 0$ 
A)  $x ^ { 2 } + 576 = 0$ 
B)  $x ^ { 2 } + 48 + 576 = 0$ 
C)  $x ^ { 2 } - 48 - 576 = 0$ 
D)  $x ^ { 2 } - 576 = 0$

Graph the solution set. - $| 2 x + 5 | + 8 = 14$

Solve the inequality. Write the solution set in interval notation. - $| - 3 x - 9 | \geq - 3$

Solve and graph the inequality. Give answer in interval notation. - $8 + 6 x + 2 \geq 5 x + 7$ $Solve and graph the inequality. Give answer in interval notation. - 8 + 6 x + 2 \geq 5 x + 7$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 1 } { x - 5 } > 0$

Determine whether or not the equation is linear. - $- 7.9 x + 1.2 = - 67.8 - 1.0 x$

The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 27 t + 176$ . Determine the number of units to be sold in order for $\mathrm { P } < 0$ (a loss is taken).

The number of non-text books read by college students ranges from 6 to 44 . Using B as the variable, write an absolute value inequality that corresponds to this range.

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

Solve the problem. -Walt made an extra $10,000 last year from a part-time job. He invested part of the money at 2% and the rest at 3.25%. He made a total of $237.50 in interest. How much was invested at 3.25%?

The position of an object moving in a straight line is given by s $s = 2 t ^ { 2 } - 3 t$ 3t, 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 9 Meters?

Decide what values of the variable cannot possibly be solutions for the equation. - $1 - \frac { 7 } { x } - \frac { 18 } { x ^ { 2 } } = 0$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $2 , - 9$

Solve the equation by the square root property. - $x ^ { 2 } = 20$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 4 } { x - 1 } + \frac { 6 x } { 1 - x } = 11$

Graph the solution set. - $| x - 5 | = 0$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } + 4 x ^ { 2 } - 9 x - 36 \geq 0$

Graph the solution set. - $| 7 x + 6 | = | 1 - 10 x |$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 5 } { 6 } - \frac { 1 } { 7 } x \right| > \frac { 2 } { 9 }$

Solve and graph the inequality. Give answer in interval notation. - $\frac { x - 2 } { 24 } \geq \frac { x - 2 } { 30 } + \frac { 1 } { 120 }$ $Solve and graph the inequality. Give answer in interval notation. - \frac { x - 2 } { 24 } \geq \frac { x - 2 } { 30 } + \frac { 1 } { 120 }$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $24 \mathrm { i } , - 24 \mathrm { i }$

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 2: Equations and Inequalities

Graph the solution set. - ∣2x+5∣+8=14| 2 x + 5 | + 8 = 14∣2x+5∣+8=14

Solve the inequality. Write the solution set in interval notation. - ∣−3x−9∣≥−3| - 3 x - 9 | \geq - 3∣−3x−9∣≥−3

Solve and graph the inequality. Give answer in interval notation. - 8+6x+2≥5x+78 + 6 x + 2 \geq 5 x + 78+6x+2≥5x+7

Solve the rational inequality. Write the solution set in interval notation. - 1x−5>0\frac { 1 } { x - 5 } > 0x−51​>0

Determine whether or not the equation is linear. - −7.9x+1.2=−67.8−1.0x- 7.9 x + 1.2 = - 67.8 - 1.0 x−7.9x+1.2=−67.8−1.0x

The profit made when ttt units are sold, t>0t > 0t>0 , is given by P=t2−27t+176P = t ^ { 2 } - 27 t + 176P=t2−27t+176 . Determine the number of units to be sold in order for P<0\mathrm { P } < 0P<0 (a loss is taken).

The number of non-text books read by college students ranges from 6 to 44 . Using B as the variable, write an absolute value inequality that corresponds to this range.

Solve and graph the inequality. Give answer in interval notation. - x5−12≤x2+2\frac { x } { 5 } - \frac { 1 } { 2 } \leq \frac { x } { 2 } + 25x​−21​≤2x​+2

Solve the problem. -Walt made an extra $10,000 last year from a part-time job. He invested part of the money at 2% and the rest at 3.25%. He made a total of $237.50 in interest. How much was invested at 3.25%?

The position of an object moving in a straight line is given by s s=2t2−3ts = 2 t ^ { 2 } - 3 ts=2t2−3t 3t, 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 9 Meters?

Decide what values of the variable cannot possibly be solutions for the equation. - 1−7x−18x2=01 - \frac { 7 } { x } - \frac { 18 } { x ^ { 2 } } = 01−x7​−x218​=0

Find the values of a, b, and c for which the quadratic equation ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - 2,−92 , - 92,−9

Solve the equation by the square root property. - x2=20x ^ { 2 } = 20x2=20

Decide what values of the variable cannot possibly be solutions for the equation. - 4x−1+6x1−x=11\frac { 4 } { x - 1 } + \frac { 6 x } { 1 - x } = 11x−14​+1−x6x​=11

Graph the solution set. - ∣x−5∣=0| x - 5 | = 0∣x−5∣=0

Solve the inequality. Write the solution set in interval notation. - x3+4x2−9x−36≥0x ^ { 3 } + 4 x ^ { 2 } - 9 x - 36 \geq 0x3+4x2−9x−36≥0

Graph the solution set. - ∣7x+6∣=∣1−10x∣| 7 x + 6 | = | 1 - 10 x |∣7x+6∣=∣1−10x∣

Solve the inequality. Write the solution set in interval notation. - ∣56−17x∣>29\left| \frac { 5 } { 6 } - \frac { 1 } { 7 } x \right| > \frac { 2 } { 9 }​65​−71​x​>92​

Solve and graph the inequality. Give answer in interval notation. - x−224≥x−230+1120\frac { x - 2 } { 24 } \geq \frac { x - 2 } { 30 } + \frac { 1 } { 120 }24x−2​≥30x−2​+1201​

Find the values of a, b, and c for which the quadratic equation ax2+bx+c=0a x ^ { 2 } + b x + c = 0ax2+bx+c=0 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - 24i,−24i24 \mathrm { i } , - 24 \mathrm { i }24i,−24i

Review of Basic Concepts

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Graph the solution set. - $| 2 x + 5 | + 8 = 14$

Solve the inequality. Write the solution set in interval notation. - $| - 3 x - 9 | \geq - 3$

Solve and graph the inequality. Give answer in interval notation. - $8 + 6 x + 2 \geq 5 x + 7$ $Solve and graph the inequality. Give answer in interval notation. - 8 + 6 x + 2 \geq 5 x + 7$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { 1 } { x - 5 } > 0$

Determine whether or not the equation is linear. - $- 7.9 x + 1.2 = - 67.8 - 1.0 x$

The profit made when $t$ units are sold, $t > 0$ , is given by $P = t ^ { 2 } - 27 t + 176$ . Determine the number of units to be sold in order for $\mathrm { P } < 0$ (a loss is taken).

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

The position of an object moving in a straight line is given by s $s = 2 t ^ { 2 } - 3 t$ 3t, 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 9 Meters?

Decide what values of the variable cannot possibly be solutions for the equation. - $1 - \frac { 7 } { x } - \frac { 18 } { x ^ { 2 } } = 0$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $2 , - 9$

Solve the equation by the square root property. - $x ^ { 2 } = 20$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 4 } { x - 1 } + \frac { 6 x } { 1 - x } = 11$

Graph the solution set. - $| x - 5 | = 0$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 3 } + 4 x ^ { 2 } - 9 x - 36 \geq 0$

Graph the solution set. - $| 7 x + 6 | = | 1 - 10 x |$

Solve the inequality. Write the solution set in interval notation. - $\left| \frac { 5 } { 6 } - \frac { 1 } { 7 } x \right| > \frac { 2 } { 9 }$

Solve and graph the inequality. Give answer in interval notation. - $\frac { x - 2 } { 24 } \geq \frac { x - 2 } { 30 } + \frac { 1 } { 120 }$ $Solve and graph the inequality. Give answer in interval notation. - \frac { x - 2 } { 24 } \geq \frac { x - 2 } { 30 } + \frac { 1 } { 120 }$

Find the values of a, b, and c for which the quadratic equation $a x ^ { 2 } + b x + c = 0$ 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $24 \mathrm { i } , - 24 \mathrm { i }$