Question 1

Solve the equation.
-$$| 5 x - 9 | = | x - 1 |$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 2 \}$ 
C)  $\left\{ - 2 , - \frac { 5 } { 3 } \right\}$ 
D)  $\left\{ 2 , \frac { 5 } { 3 } \right\}$ 
A)  $\varnothing$ 
B)  $\{ 2 \}$ 
C)  $\left\{ - 2 , - \frac { 5 } { 3 } \right\}$ 
D)  $\left\{ 2 , \frac { 5 } { 3 } \right\}$

Question 2

Solve the rational inequality. Write the solution set in interval notation.
-$$\frac { x - 7 } { x + 8 } \leq 0$$

Accepted Answer

A)  $( - 7,8 ]$ 
B)  $[ - 7,8 ]$ 
C)  $( - 8,7 ]$ 
D)  $[ - 8,7 ]$ 
A)  $( - 7,8 ]$ 
B)  $[ - 7,8 ]$ 
C)  $( - 8,7 ]$ 
D)  $[ - 8,7 ]$

Question 3

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 1 } { x } + \frac { 2 } { 11 x } = 8$$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ \frac { 3 } { 8 } \right\}$ 
C)  $\left\{ \frac { 13 } { 8 } \right\}$ 
D)  $\left\{ \frac { 13 } { 88 } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ \frac { 3 } { 8 } \right\}$ 
C)  $\left\{ \frac { 13 } { 8 } \right\}$ 
D)  $\left\{ \frac { 13 } { 88 } \right\}$

Question 4

Decide what values of the variable cannot possibly be solutions for the equation.
-A water tank can be filled in 9 minutes and emptied in 10 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

Accepted Answer

A)  $\frac { 1 } { 19 } \mathrm {~min}$ 
B)  $\frac { 1 } { 90 } \mathrm {~min}$ 
C)  $\frac { 90 } { 19 } \mathrm {~min}$ 
D)  $90 \mathrm {~min}$ 
A)  $\frac { 1 } { 19 } \mathrm {~min}$ 
B)  $\frac { 1 } { 90 } \mathrm {~min}$ 
C)  $\frac { 90 } { 19 } \mathrm {~min}$ 
D)  $90 \mathrm {~min}$

Question 5

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

Accepted Answer

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

Question 6

Write the statement as an absolute value inequality.
-$\mathrm { m }$ is no more than 9 units from 8

Accepted Answer

A)  $| m - 8 | \leq 9$ 
B)  $| m - 8 |  9$ 
A)  $| m - 8 | \leq 9$ 
B)  $| m - 8 |  9$

Question 7

Solve the inequality. Write the solution set in interval notation.
-$$| x + 8 | \geq 0$$

Accepted Answer

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

Question 8

Solve the equation using the quadratic formula.
-$$x ^ { 2 } + x + 5 = 0$$

Accepted Answer

A)  $\left\{ - \frac { 1 } { 2 } \pm \frac { \sqrt { 19 } } { 2 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } \pm \frac { \sqrt { 19 } } { 2 } \mathrm { i } \right\}$ 
C)  $\left\{ \frac { - 1 \pm \sqrt { 19 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 \pm \sqrt { 19 } } { 2 } \right\}$ 
A)  $\left\{ - \frac { 1 } { 2 } \pm \frac { \sqrt { 19 } } { 2 } \mathrm { i } \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } \pm \frac { \sqrt { 19 } } { 2 } \mathrm { i } \right\}$ 
C)  $\left\{ \frac { - 1 \pm \sqrt { 19 } } { 2 } \right\}$ 
D)  $\left\{ \frac { 1 \pm \sqrt { 19 } } { 2 } \right\}$

Question 9

Solve the problem.
-A ball is dropped from a cliff that is 432 feet high. The distance S (in feet) that it falls in t seconds is given by the formula S = 16t2. How many seconds (to tenths) will it take for the ball to hit the
Ground?

Accepted Answer

A)  11,664 sec 
B)  5.2 sec 
C)  20.4 sec 
D)  20.8 sec 
A)  11,664 sec 
B)  5.2 sec 
C)  20.4 sec 
D)  20.8 sec

Question 10

Solve the inequality. Write the solution set in interval notation.
-$$| x + 1 | > 3$$

Accepted Answer

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

Question 11

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.
-$$- 4,8$$

Accepted Answer

A)  $x ^ { 2 } + 4 x - 32 = 0$ 
B)  $x ^ { 2 } - 4 x - 32 = 0$ 
C)  $x ^ { 2 } - 32 x - 4 = 0$ 
D)  $x ^ { 2 } - 32 x + 4 = 0$ 
A)  $x ^ { 2 } + 4 x - 32 = 0$ 
B)  $x ^ { 2 } - 4 x - 32 = 0$ 
C)  $x ^ { 2 } - 32 x - 4 = 0$ 
D)  $x ^ { 2 } - 32 x + 4 = 0$

Question 12

Write the inequality in interval notation.
-$$- 5 \leq x < 3$$

Accepted Answer

A)  $( - 5,3 ]$ 
B)  $[ - 5,3 ]$ 
C)  $( - 5,3 )$ 
D)  $[ - 5,3 )$ 
A)  $( - 5,3 ]$ 
B)  $[ - 5,3 ]$ 
C)  $( - 5,3 )$ 
D)  $[ - 5,3 )$

Question 13

Simplify the power of i.
-$\mathrm { i }  ^ { 66 }$

Accepted Answer

A)  -i 
B)  -1 
C)  1 
D)  i 
A)  -i 
B)  -1 
C)  1 
D)  i

Question 14

Solve the problem.
-Jill is 18 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 kilometers per hour. They meet in 4 hours. How fast is Joe walking?

Accepted Answer

A)  $5 \mathrm {~km} / \mathrm { hr }$ 
B)  $3 \mathrm {~km} / \mathrm { hr }$ 
C)  $4 \mathrm {~km} / \mathrm { hr }$ 
D)  $1.5 \mathrm {~km} / \mathrm { hr }$ 
A)  $5 \mathrm {~km} / \mathrm { hr }$ 
B)  $3 \mathrm {~km} / \mathrm { hr }$ 
C)  $4 \mathrm {~km} / \mathrm { hr }$ 
D)  $1.5 \mathrm {~km} / \mathrm { hr }$

Question 15

Solve the equation by the zero-factor property.
-Which one of the following equations is set up for direct use of the square root property?

Accepted Answer

A)  $( 3 x + 5 ) ^ { 2 } = 6$ 
B)  $x ^ { 2 } + x = 6$ 
C)  $( 3 x + 5 ) ( x + 6 ) = 0$ 
D)  $3 x ^ { 2 } + 5 x + 6 = 0$ 
A)  $( 3 x + 5 ) ^ { 2 } = 6$ 
B)  $x ^ { 2 } + x = 6$ 
C)  $( 3 x + 5 ) ( x + 6 ) = 0$ 
D)  $3 x ^ { 2 } + 5 x + 6 = 0$

Question 16

Decide whether the statement is true or false.
--8 is a solution of 8x + 5x = -104.

Accepted Answer

A) True 
 B)False

Question 17

Solve the inequality. Write the solution set in interval notation.
-$| 3 - 7 x | > 4$

Accepted Answer

A)  $\left( - \infty , - \frac { 1 } { 7 } \right) \cup \left( - \frac { 9 } { 7 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 1 } { 7 } \right) \cup ( 1 , \infty )$ 
C)  $\left( \frac { 1 } { 7 } , - 1 \right)$ 
D)  $\left\{ - 1 , - \frac { 1 } { 7 } \right)$ 
A)  $\left( - \infty , - \frac { 1 } { 7 } \right) \cup \left( - \frac { 9 } { 7 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 1 } { 7 } \right) \cup ( 1 , \infty )$ 
C)  $\left( \frac { 1 } { 7 } , - 1 \right)$ 
D)  $\left\{ - 1 , - \frac { 1 } { 7 } \right)$

Question 18

Use these equations to convert between the two systems. $$C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$$ Round answer to the nearest tenth of a degree if necessary.
-$$F = 5 ^ { \circ }$$

Accepted Answer

A)  $\mathrm { C } = - 15 ^ { \circ }$ 
B)  $C = - 0.8 ^ { \circ }$ 
C)  $C = 20.6 ^ { \circ }$ 
D)  $\mathrm { C } = - 48.6 ^ { \circ }$ 
A)  $\mathrm { C } = - 15 ^ { \circ }$ 
B)  $C = - 0.8 ^ { \circ }$ 
C)  $C = 20.6 ^ { \circ }$ 
D)  $\mathrm { C } = - 48.6 ^ { \circ }$

Question 19

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$2 [ 3 - ( 6 - 5 x ) ] - x = - 12 + 3 ( 2 + 3 x )$$

Accepted Answer

A)  Identity; {all real numbers} 
B)  Conditional; $\{ - 6 \}$ 
C)  Conditional; $\{ 12 \}$ 
D)  Contradiction; $\varnothing$ 
A)  Identity; {all real numbers} 
B)  Conditional; $\{ - 6 \}$ 
C)  Conditional; $\{ 12 \}$ 
D)  Contradiction; $\varnothing$

Question 20

Write the inequality in interval notation.
-

Accepted Answer

A)  $( - \infty , \infty ]$ 
B)  $( - \infty , 8 )$ 
C)  $( - \infty , - 9 ]$ 
D)  $( 8 , \infty )$ 
A)  $( - \infty , \infty ]$ 
B)  $( - \infty , 8 )$ 
C)  $( - \infty , - 9 ]$ 
D)  $( 8 , \infty )$

Solve the equation. - $| 5 x - 9 | = | x - 1 |$

Solve the rational inequality. Write the solution set in interval notation. - $\frac { x - 7 } { x + 8 } \leq 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 1 } { x } + \frac { 2 } { 11 x } = 8$

Decide what values of the variable cannot possibly be solutions for the equation. -A water tank can be filled in 9 minutes and emptied in 10 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank?

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

Write the statement as an absolute value inequality. - $\mathrm { m }$ is no more than 9 units from 8

Solve the inequality. Write the solution set in interval notation. - $| x + 8 | \geq 0$

Solve the equation using the quadratic formula. - $x ^ { 2 } + x + 5 = 0$

Solve the problem. -A ball is dropped from a cliff that is 432 feet high. The distance S (in feet) that it falls in t seconds is given by the formula S = 16t2. How many seconds (to tenths) will it take for the ball to hit the Ground?

Solve the inequality. Write the solution set in interval notation. - $| x + 1 | > 3$

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. - $- 4,8$

Write the inequality in interval notation. - $- 5 \leq x < 3$

Simplify the power of i. - $\mathrm { i } ^ { 66 }$

Solve the problem. -Jill is 18 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 1.5 kilometers per hour. They meet in 4 hours. How fast is Joe walking?

Solve the equation by the zero-factor property. -Which one of the following equations is set up for direct use of the square root property?

Decide whether the statement is true or false. --8 is a solution of 8x + 5x = -104.

Solve the inequality. Write the solution set in interval notation. - $| 3 - 7 x | > 4$

Use these equations to convert between the two systems. $C = \frac { 5 } { 9 } ( F - 32 ) \quad F = \frac { 9 } { 5 } C + 32$ Round answer to the nearest tenth of a degree if necessary. - $F = 5 ^ { \circ }$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $2 [ 3 - ( 6 - 5 x ) ] - x = - 12 + 3 ( 2 + 3 x )$

Write the inequality in interval notation. -

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 the equation. - ∣5x−9∣=∣x−1∣| 5 x - 9 | = | x - 1 |∣5x−9∣=∣x−1∣

Solve the rational inequality. Write the solution set in interval notation. - x−7x+8≤0\frac { x - 7 } { x + 8 } \leq 0x+8x−7​≤0

Decide what values of the variable cannot possibly be solutions for the equation. - 1x+211x=8\frac { 1 } { x } + \frac { 2 } { 11 x } = 8x1​+11x2​=8