Question 1

Multiply or divide, as indicated. Simplify the answer.
-$$\frac { \sqrt { - 24 } } { \sqrt { 6 } }$$

Accepted Answer

A)  2 
B)  $2 \mathrm { i }$ 
C)  $- 2 \mathrm { i }$ 
D)  $- 2$ 
A)  2 
B)  $2 \mathrm { i }$ 
C)  $- 2 \mathrm { i }$ 
D)  $- 2$

Question 2

Solve the inequality. Write the solution set in interval notation.
-$$| 2 x - 5 | - 1 \geq 6$$

Accepted Answer

A)  $[ - 1,6 ]$ 
B)  $\varnothing$ 
C)  $[ 6 , \infty ]$ 
D)  $( \infty , - 1 ] \cup [ 6 , \infty )$ 
A)  $[ - 1,6 ]$ 
B)  $\varnothing$ 
C)  $[ 6 , \infty ]$ 
D)  $( \infty , - 1 ] \cup [ 6 , \infty )$

Question 3

Solve the equation.
-$$x ^ { 2 } = 4$$

Accepted Answer

A)  $\pm 2 \mathrm { i }$ 
B)  $\pm i \sqrt { 2 }$ 
C)  $\pm \sqrt { 2 }$ 
D)  $\pm 2$ 
A)  $\pm 2 \mathrm { i }$ 
B)  $\pm i \sqrt { 2 }$ 
C)  $\pm \sqrt { 2 }$ 
D)  $\pm 2$

Question 4

Decide what values of the variable cannot possibly be solutions for the equation.
-$$\frac { 5 } { x ^ { 2 } - 4 } - \frac { 3 } { x ^ { 2 } + 5 x + 6 } = \frac { 3 } { x ^ { 2 } + x - 6 }$$

Accepted Answer

A)  $\left\{ \frac { 27 } { 5 } \right\}$ 
B)  $\{ - 3 , - 2,2 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ 15 \}$ 
A)  $\left\{ \frac { 27 } { 5 } \right\}$ 
B)  $\{ - 3 , - 2,2 \}$ 
C)  $\{ 7 \}$ 
D)  $\{ 15 \}$

Question 5

Decide whether the statement is true or false.
-3 is a solution of -5x + 4x = -2x.

Accepted Answer

A) True 
 B)False

Question 6

Solve the formula for the indicated variable.
-$P = 21 + 2 w$, for $l$

Accepted Answer

A)  $1 = P - 2 w - 2$ 
B)  $1 = \frac { P } { 2 } - 2 w$ 
C)  $l = \frac { P } { 2 w + 2 }$ 
D)  $1 = \frac { P - 2 w } { 2 }$ 
A)  $1 = P - 2 w - 2$ 
B)  $1 = \frac { P } { 2 } - 2 w$ 
C)  $l = \frac { P } { 2 w + 2 }$ 
D)  $1 = \frac { P - 2 w } { 2 }$

Question 7

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$2 ( 5 x - 14 ) - 10 x + 28 = 0$$

Accepted Answer

A)  Conditional; $\{ 0 \}$ 
B)  Identity; {all real numbers} 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ 5 \}$ 
A)  Conditional; $\{ 0 \}$ 
B)  Identity; {all real numbers} 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ 5 \}$

Question 8

Decide what values of the variable cannot possibly be solutions for the equation.
-$$x = \sqrt { 2 x + 24 }$$

Accepted Answer

A)  $\{ 6 \}$ 
B)  $\{ 6 , - 4 \}$ 
C)  $\varnothing$ 
D)  $\{ 2 \}$ 
A)  $\{ 6 \}$ 
B)  $\{ 6 , - 4 \}$ 
C)  $\varnothing$ 
D)  $\{ 2 \}$

Question 9

Solve the problem.
-In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 25° less than that of angle C. Find the measure of the angles.

Accepted Answer

A)  82° , 16° and 82° 
B)  123° , 16° and 82° 
C)  123° , 16° and 41° 
D)  82° , 16° and 41° 
A)  82° , 16° and 82° 
B)  123° , 16° and 82° 
C)  123° , 16° and 41° 
D)  82° , 16° and 41°

Question 10

Solve the equation.
-$$| 7 x - 4 | = | x - 6 |$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 3 } , - \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 3 } , - \frac { 1 } { 3 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 1 } { 3 } , \frac { 5 } { 4 } \right\}$ 
A)  $\left\{ \frac { 1 } { 3 } , - \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 3 } , - \frac { 1 } { 3 } \right\}$ 
C)  $\varnothing$ 
D)  $\left\{ - \frac { 1 } { 3 } , \frac { 5 } { 4 } \right\}$

Question 11

Solve the equation.
-$| 5 x - 7 | = - 9$

Accepted Answer

A)  $\varnothing$ 
B)  $\left\{ \frac { 16 } { 5 } , \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ - \frac { 9 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 2 } { 5 } \right\}$ 
A)  $\varnothing$ 
B)  $\left\{ \frac { 16 } { 5 } , \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ - \frac { 9 } { 5 } , - \frac { 2 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 2 } { 5 } \right\}$

Question 12

Solve the problem
-The difference of the squares of two positive consecutive even integers is 68. Find the integers.

Accepted Answer

A)  14,12 
B)  16,14 
C)  16,18 
D)  18,20 
A)  14,12 
B)  16,14 
C)  16,18 
D)  18,20

Question 13

Solve the rational inequality. Write the solution set in interval notation.
-A retailer knows that n games can be sold in a month if the price is 20 - 0.3n dollars per game. If he buys each game for $2, and if he wishes to make a profit of at least $240 per month on sales of this
Game, how many games must he sell each month?

Accepted Answer

A)  $20 \leq n \leq 40$ 
B)  $20 \leq n \leq 60$ 
C)  $20 \leq n \leq 20$ 
D)  $20 \leq n \leq 30$ 
A)  $20 \leq n \leq 40$ 
B)  $20 \leq n \leq 60$ 
C)  $20 \leq n \leq 20$ 
D)  $20 \leq n \leq 30$

Question 14

Solve the equation by the zero-factor property.
-$$x ^ { 2 } + 4 x - 45 = 0$$

Accepted Answer

A)  $\{ 7 , - 7 \}$ 
B)  $\{ - 36 , - 9 \}$ 
C)  $\{ - 5,9 \}$ 
D)  $\{ 5 , - 9 \}$ 
A)  $\{ 7 , - 7 \}$ 
B)  $\{ - 36 , - 9 \}$ 
C)  $\{ - 5,9 \}$ 
D)  $\{ 5 , - 9 \}$

Question 15

Solve the problem.
-Mardi received an inheritance of $40,000. She invested part at 1.5% and deposited the remainder in tax-free bonds at 2%. Her total annual income from the investments was $650. Find the amount
Invested at 1.5%.

Accepted Answer

A)  $39,350 
B)  $15,000 
C)  $29,000 
D)  $30,000 
A)  $39,350 
B)  $15,000 
C)  $29,000 
D)  $30,000

Question 16

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$w ^ { 2 } - 3 w + 8 = 0$

Accepted Answer

A)  Two distinct rational solutions 
B)  Two distinct irrational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct nonreal complex solutions 
A)  Two distinct rational solutions 
B)  Two distinct irrational solutions 
C)  One rational solution (a double solution) 
D)  Two distinct nonreal complex solutions

Question 17

Decide whether or not the equations are equivalent.
-$\begin{array} { l } 
2 x - 3 = 7 \
- 2 x - 3 = 7
\end{array}$

Accepted Answer

A)  Equivalent 
B)  Not equivalent 
A)  Equivalent 
B)  Not equivalent

Question 18

Solve the cubic equation using factoring and the quadratic formula.
-$$x ^ { 3 } + 64 = 0$$

Accepted Answer

A)  $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 3 } \}$ 
B)  $\{ - 4 , - 2 \pm 2 \mathrm { i } \sqrt { 6 } \}$ 
C)  $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 5 } \}$ 
D)  $\{ - 4 , - 2 \pm 2 i \}$ 
A)  $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 3 } \}$ 
B)  $\{ - 4 , - 2 \pm 2 \mathrm { i } \sqrt { 6 } \}$ 
C)  $\{ - 4,2 \pm 2 \mathrm { i } \sqrt { 5 } \}$ 
D)  $\{ - 4 , - 2 \pm 2 i \}$

Question 19

Solve the problem.
-The length of a rectangle is 6 inches more than its width. If 3 inches are taken from the length and added to the width, the figure becomes a square with an area of 361 square inches. What are the
Dimensions of the original figure?

Accepted Answer

A)  16 in. by 19 in. 
B)  13 in. by 19 in. 
C)  19 in. by 19 in. 
D)  16 in. by 22 in. 
A)  16 in. by 19 in. 
B)  13 in. by 19 in. 
C)  19 in. by 19 in. 
D)  16 in. by 22 in.

Question 20

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set.
-$$10 x + 91 = 2 ( 5 x + 41 )$$

Accepted Answer

A)  Conditional; $\{ 5 \}$ 
B)  Identity; {all real numbers} 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ - 5 \}$ 
A)  Conditional; $\{ 5 \}$ 
B)  Identity; {all real numbers} 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{ - 5 \}$

Multiply or divide, as indicated. Simplify the answer. - $\frac { \sqrt { - 24 } } { \sqrt { 6 } }$

Solve the inequality. Write the solution set in interval notation. - $| 2 x - 5 | - 1 \geq 6$

Solve the equation. - $x ^ { 2 } = 4$

Decide what values of the variable cannot possibly be solutions for the equation. - $\frac { 5 } { x ^ { 2 } - 4 } - \frac { 3 } { x ^ { 2 } + 5 x + 6 } = \frac { 3 } { x ^ { 2 } + x - 6 }$

Decide whether the statement is true or false. -3 is a solution of -5x + 4x = -2x.

Solve the formula for the indicated variable. - $P = 21 + 2 w$ , for $l$

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $2 ( 5 x - 14 ) - 10 x + 28 = 0$

Decide what values of the variable cannot possibly be solutions for the equation. - $x = \sqrt { 2 x + 24 }$

Solve the problem. -In triangle ABC, angle A is three times as large as angle C. The measure of angle B is 25° less than that of angle C. Find the measure of the angles.

Solve the equation. - $| 7 x - 4 | = | x - 6 |$

Solve the equation. - $| 5 x - 7 | = - 9$

Solve the problem -The difference of the squares of two positive consecutive even integers is 68. Find the integers.

Solve the equation by the zero-factor property. - $x ^ { 2 } + 4 x - 45 = 0$

Solve the problem. -Mardi received an inheritance of $40,000. She invested part at 1.5% and deposited the remainder in tax-free bonds at 2%. Her total annual income from the investments was $650. Find the amount Invested at 1.5%.

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $w ^ { 2 } - 3 w + 8 = 0$

Decide whether or not the equations are equivalent. - 2x-3=7 -2x-3=7

Solve the cubic equation using factoring and the quadratic formula. - $x ^ { 3 } + 64 = 0$

Solve the problem. -The length of a rectangle is 6 inches more than its width. If 3 inches are taken from the length and added to the width, the figure becomes a square with an area of 361 square inches. What are the Dimensions of the original figure?

Decide whether the equation is an identity, a conditional equation, or a contradiction. Give the solution set. - $10 x + 91 = 2 ( 5 x + 41 )$

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

Multiply or divide, as indicated. Simplify the answer. - −246\frac { \sqrt { - 24 } } { \sqrt { 6 } }6​−24​​

Solve the inequality. Write the solution set in interval notation. - ∣2x−5∣−1≥6| 2 x - 5 | - 1 \geq 6∣2x−5∣−1≥6

Solve the equation. - x2=4x ^ { 2 } = 4x2=4

Decide what values of the variable cannot possibly be solutions for the equation. - 5x2−4−3x2+5x+6=3x2+x−6\frac { 5 } { x ^ { 2 } - 4 } - \frac { 3 } { x ^ { 2 } + 5 x + 6 } = \frac { 3 } { x ^ { 2 } + x - 6 }x2−45​−x2+5x+63​=x2+x−63​