Question 1

Express the set in the simplest interval form.
-$(-7,4) \cup[0,9]$

Accepted Answer

A)  $(-7,9]$ 
B)  $(-7,4)$ 
C)  $[0,9]$ 
D)  $[0,4)$ 
A)  $(-7,9]$ 
B)  $(-7,4)$ 
C)  $[0,9]$ 
D)  $[0,4)$

Question 2

Solve the problem.
-What is the area of a square with side $2.2 \mathrm{~cm}$ ?

Accepted Answer

A)  $10 \mathrm{~cm}^{2}$ 
B)  $19.36 \mathrm{~cm}^{2}$ 
C)  $4.84 \mathrm{~cm}^{2}$ 
D)  $4.4 \mathrm{~cm}^{2}$ 
A)  $10 \mathrm{~cm}^{2}$ 
B)  $19.36 \mathrm{~cm}^{2}$ 
C)  $4.84 \mathrm{~cm}^{2}$ 
D)  $4.4 \mathrm{~cm}^{2}$

Question 3

Each of six decorators has to paint a room (walls only) and put a wallpaper border around the room at the ceiling. One gallon of paint covers $400 \mathrm{sq} \mathrm{ft}$, and one roll of border contains five yards. Each decorator has one gallon of paint and three rolls of border.
-The list gives the name of each decorator and the size of the room.

Give the names of the decorators who will not have enough paint, but will have enough border for their rooms. (Assume a ceiling height of 8 ' for each room.)

Accepted Answer

A)  $\{$ Mary, Roger $\}$ 
B)  $\{$ Irina, Sergey$\}$ 
C)  $\{$ Juanita, Jose $\}$ 
D)  None 
A)  $\{$ Mary, Roger $\}$ 
B)  $\{$ Irina, Sergey$\}$ 
C)  $\{$ Juanita, Jose $\}$ 
D)  None

Question 4

Solve the problem.
-There were 35,000 people at a ball game in Los Angeles. The day's receipts were $\$ 253,000$. How many people paid $\$ 11.00$ for reserved seats and how many paid $\$ 5.00$ for general admission?

Accepted Answer

A)  13,000 paid $\$ 11$ and 22,000 paid $\$ 5$ 
B)  19,500 paid $\$ 11$ and 15,500 paid $\$ 5$ 
C)  22,000 paid $\$ 11$ and 13,000 paid $\$ 5$ 
D)  15,500 paid $\$ 11$ and 19,500 paid $\$ 5$ 
A)  13,000 paid $\$ 11$ and 22,000 paid $\$ 5$ 
B)  19,500 paid $\$ 11$ and 15,500 paid $\$ 5$ 
C)  22,000 paid $\$ 11$ and 13,000 paid $\$ 5$ 
D)  15,500 paid $\$ 11$ and 19,500 paid $\$ 5$

Question 5

Suppose the formula $A=2 \pi r h+2 \pi r^{2}$ is solved for $r$ with the following result: $r=$ $\frac{\mathrm{A}}{2 \pi \mathrm{h}+2 \pi \mathrm{r}}$. Is this an acceptable solution? Explain.

Accepted Answer

No. The variable r s

Question 6

Provide an appropriate response.
-Determine which of the following is used to solve the inequality $|a x+b|>c$, for $c>0$.

Accepted Answer

A) $a x+b>c$ or $a x+b\mathrm{c}$ or $\mathrm{ax}+\mathrm{b}>-\mathrm{c}$ C) $a x+b-c$ D) $a x+b>c$ and $a x+b<-c$ A) $a x+b>c$ or $a x+b\mathrm{c}$ or $\mathrm{ax}+\mathrm{b}>-\mathrm{c}$ C) $a x+b-c$ D) $a x+b>c$ and $a x+b<-c$

Question 7

Use the variable $x$ for the unknown, and write an equation representing the verbal sentence. Then solve the problem.
-When $\frac{1}{4}$ of a number is added to 20 , the result is 29 .

Accepted Answer

A)  $\frac{1}{4} x-20=29 ; 196$ 
B)  $29+\frac{1}{4} \mathrm{x}=20 ; 36$ 
C)  $\frac{1}{4}+x=29 ; 29$ 
D)  $20+\frac{1}{4} x=29 ; 36$ 
A)  $\frac{1}{4} x-20=29 ; 196$ 
B)  $29+\frac{1}{4} \mathrm{x}=20 ; 36$ 
C)  $\frac{1}{4}+x=29 ; 29$ 
D)  $20+\frac{1}{4} x=29 ; 36$

Question 8

Solve the problem.
-A chemical solution contains $8 \%$ salt. How much salt is in $4 \mathrm{ml}$ of solution? Round your answer to three decimal places, if necessary.

Accepted Answer

A)  $50 \mathrm{ml}$ 
B)  $5 \mathrm{ml}$ 
C)  $0.32 \mathrm{ml}$ 
D)  $3.2 \mathrm{ml}$ 
A)  $50 \mathrm{ml}$ 
B)  $5 \mathrm{ml}$ 
C)  $0.32 \mathrm{ml}$ 
D)  $3.2 \mathrm{ml}$

Question 9

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
-$5(2 \mathrm{f}-31)=10 \mathrm{f}-155$

Accepted Answer

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

Question 10

Solve the problem.
-Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 3.5 kilometers per hour. They meet in 5 hours. How fast is Brenda walking?

Accepted Answer

A)  3.5 kilometers per hour 
B)  2 kilometers per hour 
C)  3 kilometers per hour 
D)  4 kilometers per hour 
A)  3.5 kilometers per hour 
B)  2 kilometers per hour 
C)  3 kilometers per hour 
D)  4 kilometers per hour

Question 11

Which of the following is not a correct answer when the formula $V=\frac{1}{3} \pi r^{2} h$ is solved for $h$ ?

Accepted Answer

A)  $3\biggl(\frac{\mathrm{V}}{\pi \mathrm{r}^{2}}\biggl)$ 
B)  $\frac{3 \mathrm{~V}}{\pi \mathrm{r}^{2}}$ 
C)  $\frac{1}{3}\biggl(\frac{\mathrm{V}}{\pi \mathrm{r}^{2}}\biggl)$ 
D)  $\frac{\mathrm{V}}{\frac{1}{3} \pi \mathrm{r}^{2}}$ 
A)  $3\biggl(\frac{\mathrm{V}}{\pi \mathrm{r}^{2}}\biggl)$ 
B)  $\frac{3 \mathrm{~V}}{\pi \mathrm{r}^{2}}$ 
C)  $\frac{1}{3}\biggl(\frac{\mathrm{V}}{\pi \mathrm{r}^{2}}\biggl)$ 
D)  $\frac{\mathrm{V}}{\frac{1}{3} \pi \mathrm{r}^{2}}$

Question 12

Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation.
-$|0.5 x-5.3|+0.2 \geq 0.8$

Accepted Answer

A)  $(-\infty, 9.4] \cup[11.8, \infty)$ 
B)  $(-\infty, 9.4] \cap[11.8, \infty)$ 
C)  $(9.4,11.8)$ 
D)  $\{9.4,11.8\}$ 
A)  $(-\infty, 9.4] \cup[11.8, \infty)$ 
B)  $(-\infty, 9.4] \cap[11.8, \infty)$ 
C)  $(9.4,11.8)$ 
D)  $\{9.4,11.8\}$

Question 13

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
-$12 \mathrm{k}+186=4(3 \mathrm{k}+45)$

Accepted Answer

A)  Conditional; $\{3\}$ 
B)  Contradiction; $\varnothing$ 
C)  Identity; {all real numbers} 
D)  Conditional; $\{-3\}$ 
A)  Conditional; $\{3\}$ 
B)  Contradiction; $\varnothing$ 
C)  Identity; {all real numbers} 
D)  Conditional; $\{-3\}$

Question 14

Solve the inequality. Give the solution set in both interval and graph forms.
-$\frac{7 x-4}{9}<\frac{67}{7}$

Accepted Answer

A)  $ \left(\frac{67}{7}, \infty\right) $
  
B)  $ \left(-\infty, \frac{631}{49}\right) $
  
C)  $ \left(\frac{631}{49}, \infty\right) $
  
D)  $ \left(-\infty, \frac{67}{7}\right) $
  
A)  $ \left(\frac{67}{7}, \infty\right) $
  
B)  $ \left(-\infty, \frac{631}{49}\right) $
  
C)  $ \left(\frac{631}{49}, \infty\right) $
  
D)  $ \left(-\infty, \frac{67}{7}\right) $

Question 15

Solve the inequality and graph the solution set.
-$|x| \leq 7$

Accepted Answer

A)  $[-7,7]$
  
B)  $(-\infty, 7]$
  
C)  $(-\infty,-7] \cup[7, \infty)$
  
D)  $(-\infty,-7]$
  
A)  $[-7,7]$
  
B)  $(-\infty, 7]$
  
C)  $(-\infty,-7] \cup[7, \infty)$
  
D)  $(-\infty,-7]$

Question 16

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
-$2[3-(2-5 r)]-r=-4+3(2+3 r)$

Accepted Answer

A)  Identity; {all real numbers} 
B)  Conditional; $\{4\}$ 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{-2\}$ 
A)  Identity; {all real numbers} 
B)  Conditional; $\{4\}$ 
C)  Contradiction; $\varnothing$ 
D)  Conditional; $\{-2\}$

Question 17

Express the set in the simplest interval form.
-$(-4,6] \cap(-2, \infty)$

Accepted Answer

A)  $[-2,6]$ 
B)  $(-4, \infty)$ 
C)  $(-2,6]$ 
D)  $(-4,6]$ 
A)  $[-2,6]$ 
B)  $(-4, \infty)$ 
C)  $(-2,6]$ 
D)  $(-4,6]$

Question 18

Solve the equation.
-$\frac{r+6}{5}=\frac{r+8}{7}$

Accepted Answer

A)  $\{-1\}$ 
B)  $\{1\}$ 
C)  $\{2\}$ 
D)  $\{-2\}$ 
A)  $\{-1\}$ 
B)  $\{1\}$ 
C)  $\{2\}$ 
D)  $\{-2\}$

Question 19

For the compound inequality, decide whether intersection or union should be used. Then give the solution set in both interval and graph forms.
-$x \geq-9$ and $x<-4$

Accepted Answer

A)  Intersection; $[-9,-4)$
  
B)  Union; $(-\infty, \infty)$
  
C)  Intersection; $(-9, \infty)$
  
D)  Intersection; $\varnothing$
  
A)  Intersection; $[-9,-4)$
  
B)  Union; $(-\infty, \infty)$
  
C)  Intersection; $(-9, \infty)$
  
D)  Intersection; $\varnothing$

Question 20

The union of the sets $(-\infty, 23]$ and $(23, \infty)$ is $(-\infty, \infty)$

Accepted Answer

A) True 
 B)False

Express the set in the simplest interval form. - $(-7,4) \cup[0,9]$

Solve the problem. -What is the area of a square with side $2.2 \mathrm{~cm}$ ?

Solve the problem. -There were 35,000 people at a ball game in Los Angeles. The day's receipts were $\$ 253,000$ . How many people paid $\$ 11.00$ for reserved seats and how many paid $\$ 5.00$ for general admission?

Suppose the formula $A=2 \pi r h+2 \pi r^{2}$ is solved for $r$ with the following result: $r=$ $\frac{\mathrm{A}}{2 \pi \mathrm{h}+2 \pi \mathrm{r}}$ . Is this an acceptable solution? Explain.

Provide an appropriate response. -Determine which of the following is used to solve the inequality $|a x+b|>c$ , for $c>0$ .

Use the variable $x$ for the unknown, and write an equation representing the verbal sentence. Then solve the problem. -When $\frac{1}{4}$ of a number is added to 20 , the result is 29 .

Solve the problem. -A chemical solution contains $8 \%$ salt. How much salt is in $4 \mathrm{ml}$ of solution? Round your answer to three decimal places, if necessary.

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $5(2 \mathrm{f}-31)=10 \mathrm{f}-155$

Solve the problem. -Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 3.5 kilometers per hour. They meet in 5 hours. How fast is Brenda walking?

Which of the following is not a correct answer when the formula $V=\frac{1}{3} \pi r^{2} h$ is solved for $h$ ?

Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation. - $|0.5 x-5.3|+0.2 \geq 0.8$

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $12 \mathrm{k}+186=4(3 \mathrm{k}+45)$

Solve the inequality. Give the solution set in both interval and graph forms. - $\frac{7 x-4}{9}<\frac{67}{7}$ $Solve the inequality. Give the solution set in both interval and graph forms. - \frac{7 x-4}{9}<\frac{67}{7}$

Solve the inequality and graph the solution set. - $|x| \leq 7$ $Solve the inequality and graph the solution set. - |x| \leq 7$

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $2[3-(2-5 r)]-r=-4+3(2+3 r)$

Express the set in the simplest interval form. - $(-4,6] \cap(-2, \infty)$

Solve the equation. - $\frac{r+6}{5}=\frac{r+8}{7}$

The union of the sets $(-\infty, 23]$ and $(23, \infty)$ is $(-\infty, \infty)$

Review of the Real Number System

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 2: Linear Equations, Inequalities, and Applications

Express the set in the simplest interval form. - (−7,4)∪[0,9](-7,4) \cup[0,9](−7,4)∪[0,9]

Solve the problem. -What is the area of a square with side 2.2 cm2.2 \mathrm{~cm}2.2 cm ?

Solve the problem. -There were 35,000 people at a ball game in Los Angeles. The day's receipts were $253,000\$ 253,000$253,000 . How many people paid $11.00\$ 11.00$11.00 for reserved seats and how many paid $5.00\$ 5.00$5.00 for general admission?

Suppose the formula A=2πrh+2πr2A=2 \pi r h+2 \pi r^{2}A=2πrh+2πr2 is solved for rrr with the following result: r=r=r= A2πh+2πr\frac{\mathrm{A}}{2 \pi \mathrm{h}+2 \pi \mathrm{r}}2πh+2πrA​ . Is this an acceptable solution? Explain.

Provide an appropriate response. -Determine which of the following is used to solve the inequality ∣ax+b∣>c|a x+b|>c∣ax+b∣>c , for c>0c>0c>0 .

Use the variable xxx for the unknown, and write an equation representing the verbal sentence. Then solve the problem. -When 14\frac{1}{4}41​ of a number is added to 20 , the result is 29 .

Solve the problem. -A chemical solution contains 8%8 \%8% salt. How much salt is in 4ml4 \mathrm{ml}4ml of solution? Round your answer to three decimal places, if necessary.

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - 5(2f−31)=10f−1555(2 \mathrm{f}-31)=10 \mathrm{f}-1555(2f−31)=10f−155

Solve the problem. -Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 3.5 kilometers per hour. They meet in 5 hours. How fast is Brenda walking?

Which of the following is not a correct answer when the formula V=13πr2hV=\frac{1}{3} \pi r^{2} hV=31​πr2h is solved for hhh ?

Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation. - ∣0.5x−5.3∣+0.2≥0.8|0.5 x-5.3|+0.2 \geq 0.8∣0.5x−5.3∣+0.2≥0.8

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - 12k+186=4(3k+45)12 \mathrm{k}+186=4(3 \mathrm{k}+45)12k+186=4(3k+45)

Solve the inequality. Give the solution set in both interval and graph forms. - 7x−49<677\frac{7 x-4}{9}<\frac{67}{7}97x−4​<767​

Solve the inequality and graph the solution set. - ∣x∣≤7|x| \leq 7∣x∣≤7

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - 2[3−(2−5r)]−r=−4+3(2+3r)2[3-(2-5 r)]-r=-4+3(2+3 r)2[3−(2−5r)]−r=−4+3(2+3r)

Express the set in the simplest interval form. - (−4,6]∩(−2,∞)(-4,6] \cap(-2, \infty)(−4,6]∩(−2,∞)

Solve the equation. - r+65=r+87\frac{r+6}{5}=\frac{r+8}{7}5r+6​=7r+8​

For the compound inequality, decide whether intersection or union should be used. Then give the solution set in both interval and graph forms. - x≥−9x \geq-9x≥−9 and x<−4x<-4x<−4

The union of the sets (−∞,23](-\infty, 23](−∞,23] and (23,∞)(23, \infty)(23,∞) is (−∞,∞)(-\infty, \infty)(−∞,∞)

Review of the Real Number System

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Express the set in the simplest interval form. - $(-7,4) \cup[0,9]$

Solve the problem. -What is the area of a square with side $2.2 \mathrm{~cm}$ ?

Solve the problem. -There were 35,000 people at a ball game in Los Angeles. The day's receipts were $\$ 253,000$ . How many people paid $\$ 11.00$ for reserved seats and how many paid $\$ 5.00$ for general admission?

Suppose the formula $A=2 \pi r h+2 \pi r^{2}$ is solved for $r$ with the following result: $r=$ $\frac{\mathrm{A}}{2 \pi \mathrm{h}+2 \pi \mathrm{r}}$ . Is this an acceptable solution? Explain.

Provide an appropriate response. -Determine which of the following is used to solve the inequality $|a x+b|>c$ , for $c>0$ .

Use the variable $x$ for the unknown, and write an equation representing the verbal sentence. Then solve the problem. -When $\frac{1}{4}$ of a number is added to 20 , the result is 29 .

Solve the problem. -A chemical solution contains $8 \%$ salt. How much salt is in $4 \mathrm{ml}$ of solution? Round your answer to three decimal places, if necessary.

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $5(2 \mathrm{f}-31)=10 \mathrm{f}-155$

Which of the following is not a correct answer when the formula $V=\frac{1}{3} \pi r^{2} h$ is solved for $h$ ?

Solve the given equation or inequality. If an equation is given, then write the solution set in set notation. If an inequality is given, then write the solution set in interval notation. - $|0.5 x-5.3|+0.2 \geq 0.8$

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $12 \mathrm{k}+186=4(3 \mathrm{k}+45)$

Solve the inequality. Give the solution set in both interval and graph forms. - $\frac{7 x-4}{9}<\frac{67}{7}$ $Solve the inequality. Give the solution set in both interval and graph forms. - \frac{7 x-4}{9}<\frac{67}{7}$

Solve the inequality and graph the solution set. - $|x| \leq 7$ $Solve the inequality and graph the solution set. - |x| \leq 7$

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $2[3-(2-5 r)]-r=-4+3(2+3 r)$

Express the set in the simplest interval form. - $(-4,6] \cap(-2, \infty)$

Solve the equation. - $\frac{r+6}{5}=\frac{r+8}{7}$

The union of the sets $(-\infty, 23]$ and $(23, \infty)$ is $(-\infty, \infty)$