Question 1

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
-$-15 s+130+5(3 s-25)=0$

Accepted Answer

A)  Identity; {all real numbers} 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{1\}$ 
D)  Conditional; $\{3\}$ 
A)  Identity; {all real numbers} 
B)  Contradiction; $\varnothing$ 
C)  Conditional; $\{1\}$ 
D)  Conditional; $\{3\}$

Question 2

Use the variable $x$ for the unknown, and write an equation representing the verbal sentence. Then solve the problem.
-When $50 \%$ of a number is subtracted from 70 , the result is 2 less than the number.

Accepted Answer

A)  $70+0.5 x=x-2 ; 144$ 
B)  $70-50=x-2 ; 22$ 
C)  $70-0.5 x=x-2 ; 48$ 
D)  $0.5 \mathrm{x}-70=\mathrm{x}-2 ;-136$ 
A)  $70+0.5 x=x-2 ; 144$ 
B)  $70-50=x-2 ; 22$ 
C)  $70-0.5 x=x-2 ; 48$ 
D)  $0.5 \mathrm{x}-70=\mathrm{x}-2 ;-136$

Question 3

Solve the equation.
-$|\mathrm{n}-9|=|1-\mathrm{n}|$

Accepted Answer

A)  $\{10\}$ 
B)  $\{5\}$ 
C)  $\{-4\}$ 
D)  $\varnothing$ 
A)  $\{10\}$ 
B)  $\{5\}$ 
C)  $\{-4\}$ 
D)  $\varnothing$

Question 4

Solve the problem involving consecutive integers.
-The sum of the page numbers on the facing pages of a book is 313 . Find the larger page number.

Accepted Answer

A)  155 
B)  167 
C)  152 
D)  157 
A)  155 
B)  167 
C)  152 
D)  157

Question 5

Solve the equation for the specified variable. Use the distributive property to factor as necessary.
-$-6 k+a r=r-9 y$ for $r$

Accepted Answer

A)  $r=\frac{-6 k+a}{1-9 y}$ or $r=\frac{6 k-a}{9 y-1}$ 
B)  $r=\frac{6 k-9 y}{a-1}$ or $r=\frac{-6 k+9 y}{1-a}$ 
C)  $r=\frac{a-1}{6 k-9 y}$ or $r=\frac{1-a}{-6 k+9 y}$ 
D)  $r=\frac{-6 k+9 y}{a-1}$ or $r=\frac{6 k-9 y}{1-a}$ 
A)  $r=\frac{-6 k+a}{1-9 y}$ or $r=\frac{6 k-a}{9 y-1}$ 
B)  $r=\frac{6 k-9 y}{a-1}$ or $r=\frac{-6 k+9 y}{1-a}$ 
C)  $r=\frac{a-1}{6 k-9 y}$ or $r=\frac{1-a}{-6 k+9 y}$ 
D)  $r=\frac{-6 k+9 y}{a-1}$ or $r=\frac{6 k-9 y}{1-a}$

Question 6

Let A {q, s, u, v, w, x, y, z}, B {q, s, y, z}, C {v, w, x, y, z}, and D {s}. Specify the following set.
-$A \cup B$

Accepted Answer

A)  $\{\mathrm{v}, \mathrm{x}\}$ 
B)  $\{\mathrm{s}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{z}\}$ 
C)  $\{\mathrm{s}, \mathrm{u}, \mathrm{w}\}$ 
D)  $\{\mathrm{q}, \mathrm{s}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{y}, \mathrm{z}\}$ or $A$ 
A)  $\{\mathrm{v}, \mathrm{x}\}$ 
B)  $\{\mathrm{s}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{z}\}$ 
C)  $\{\mathrm{s}, \mathrm{u}, \mathrm{w}\}$ 
D)  $\{\mathrm{q}, \mathrm{s}, \mathrm{u}, \mathrm{v}, \mathrm{w}, \mathrm{x}, \mathrm{y}, \mathrm{z}\}$ or $A$

Question 7

Solve the problem.
-Janet drove $284 \mathrm{~km}$, and the trip took $4 \mathrm{hr}$. At what average rate was Janet traveling?

Accepted Answer

A)  $71 \mathrm{~km} / \mathrm{hr}$ 
B)  $\frac{1}{71} \mathrm{~km} / \mathrm{hr}$ 
C)  $72 \mathrm{~km} / \mathrm{hr}$ 
D)  $1136 \mathrm{~km} / \mathrm{hr}$ 
A)  $71 \mathrm{~km} / \mathrm{hr}$ 
B)  $\frac{1}{71} \mathrm{~km} / \mathrm{hr}$ 
C)  $72 \mathrm{~km} / \mathrm{hr}$ 
D)  $1136 \mathrm{~km} / \mathrm{hr}$

Question 8

Solve the problem.
-A plane flies 500 miles with the wind and 300 miles against the wind in the same length of time. If the speed of the wind is $23 \mathrm{mph}$, what is the speed of the plane in still air?

Accepted Answer

A)  $92 \mathrm{mph}$ 
B)  $97 \mathrm{mph}$ 
C)  $82 \mathrm{mph}$ 
D)  $117 \mathrm{mph}$ 
A)  $92 \mathrm{mph}$ 
B)  $97 \mathrm{mph}$ 
C)  $82 \mathrm{mph}$ 
D)  $117 \mathrm{mph}$

Question 9

Solve the equation.
-$ 0.08x+0.13(x+1800)=360$

Accepted Answer

A)  $\{6000\}$ 
B)  $\{60\}$ 
C)  $\{60,000\}$ 
D)  $\{600\}$ 
A)  $\{6000\}$ 
B)  $\{60\}$ 
C)  $\{60,000\}$ 
D)  $\{600\}$

Question 10

Solve the problem.
-Miraculous Music, Inc. finds that the cost to make $x$ compact discs is $C=13 x+12,702$, while the revenue produced from them is $\mathrm{R}=17 \mathrm{x}$ ( $\mathrm{C}$ and $\mathrm{R}$ are in dollars). What is the smallest whole number of compact discs, $x$, that must be sold for the company to show a profit?

Accepted Answer

A)  424 
B)  381,060 
C)  3176 
D)  50,808 
A)  424 
B)  381,060 
C)  3176 
D)  50,808

Question 11

Solve the problem.
-Which one of the following inequalities is equivalent to $z \geq-6$ ?

Accepted Answer

A)  $-2 z \leq-12$ 
B)  $-2 \mathrm{z} \leq 12$ 
C)  $-2 z \geq 12$ 
D)  $-2 z \geq-12$ 
A)  $-2 z \leq-12$ 
B)  $-2 \mathrm{z} \leq 12$ 
C)  $-2 z \geq 12$ 
D)  $-2 z \geq-12$

Question 12

For the compound inequality, give the solution set in both interval and graph forms.
-$11 \leq 2 x+5$ and $9 x+5<68$

Accepted Answer

A)  $(3,7]$
  
B)  $(3,7)$
  
C)  $[3,7]$
  
D)  $[3,7)$
  
A)  $(3,7]$
  
B)  $(3,7)$
  
C)  $[3,7]$
  
D)  $[3,7)$

Question 13

Solve the equation or inequality.
-$|z-6| \geq 0$

Accepted Answer

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

Question 14

If $k<0$, what is the solution set of $|3 f+1|< k$

Accepted Answer

A)  $\varnothing$ 
B)  $\left(-\frac{\mathrm{k}+1}{3}, \frac{\mathrm{k}+1}{3}\right)$ 
C)  $(-\infty, \infty)$ 
D)  $\{0\}$ 
A)  $\varnothing$ 
B)  $\left(-\frac{\mathrm{k}+1}{3}, \frac{\mathrm{k}+1}{3}\right)$ 
C)  $(-\infty, \infty)$ 
D)  $\{0\}$

Question 15

For the compound inequality, give the solution set in both interval and graph forms.
-$12 x-8<4 x$ or $-2 x \leq-6$

Accepted Answer

A)  $(-\infty, 1) \cup[3, \infty)$
  
B)  $[1,3]$
  
C)  $(1,3)$
  
D)  $\varnothing$
  
A)  $(-\infty, 1) \cup[3, \infty)$
  
B)  $[1,3]$
  
C)  $(1,3)$
  
D)  $\varnothing$

Question 16

Solve the inequality and graph the solution set.
-$|7 y-9|>-8$

Accepted Answer

A)  $\varnothing$
  
B)  $\left(\frac{1}{7}, \frac{17}{7}\right)$
  
C)  $(-\infty, \infty)$
  
D)  $\left(\frac{1}{7}, \infty\right)$
  
A)  $\varnothing$
  
B)  $\left(\frac{1}{7}, \frac{17}{7}\right)$
  
C)  $(-\infty, \infty)$
  
D)  $\left(\frac{1}{7}, \infty\right)$

Question 17

For the compound inequality, give the solution set in both interval and graph forms.
-$4 x-10 \leq 18$ and $2 x-1 \geq 13$

Accepted Answer

A)  $(7, \infty)$ 
  
B)  $[7, \infty)$
  
C)  $(-\infty, 7)$
  
D)  $\{7\}$
  
A)  $(7, \infty)$ 
  
B)  $[7, \infty)$
  
C)  $(-\infty, 7)$
  
D)  $\{7\}$

Question 18

Solve the inequality and graph the solution set.
-$|m+1|<0$

Accepted Answer

A)  $ (-\infty,-1) $
  
B)  $ (1, \infty) $
  
C)  $ \varnothing $
  
D)  $ (1,-1) $
  
A)  $ (-\infty,-1) $
  
B)  $ (1, \infty) $
  
C)  $ \varnothing $
  
D)  $ (1,-1) $

Question 19

Solve the inequality. Give the solution set in both interval and graph forms.
-$\frac{4x + 6}{-7} < -\frac{17}{2}$

Accepted Answer

A)  $ \left(-\infty,-\frac{17}{2}\right) $
  
B)  $ \left(\frac{107}{8}, \infty\right) $
  
C)  $ \left(\frac{107}{2}, \infty\right) $
  
D)  $ \left(-\frac{17}{8}, \infty\right) $
  
A)  $ \left(-\infty,-\frac{17}{2}\right) $
  
B)  $ \left(\frac{107}{8}, \infty\right) $
  
C)  $ \left(\frac{107}{2}, \infty\right) $
  
D)  $ \left(-\frac{17}{8}, \infty\right) $

Question 20

Solve the investment problem.
-Walt made an extra $\$ 5000$ last year from a part-time job. He invested part of the money at $10 \%$ and the rest at $8 \%$. He made a total of $\$ 420$ in interest. How much was invested at $8 \%$ ?

Accepted Answer

A)  $\$ 1000$ 
B)  $\$ 3000$ 
C)  $\$ 4000$ 
D)  $\$ 2500$ 
A)  $\$ 1000$ 
B)  $\$ 3000$ 
C)  $\$ 4000$ 
D)  $\$ 2500$

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $-15 s+130+5(3 s-25)=0$

Use the variable $x$ for the unknown, and write an equation representing the verbal sentence. Then solve the problem. -When $50 \%$ of a number is subtracted from 70 , the result is 2 less than the number.

Solve the equation. - $|\mathrm{n}-9|=|1-\mathrm{n}|$

Solve the problem involving consecutive integers. -The sum of the page numbers on the facing pages of a book is 313 . Find the larger page number.

Solve the equation for the specified variable. Use the distributive property to factor as necessary. - $-6 k+a r=r-9 y$ for $r$

Let A {q, s, u, v, w, x, y, z}, B {q, s, y, z}, C {v, w, x, y, z}, and D {s}. Specify the following set. - $A \cup B$

Solve the problem. -Janet drove $284 \mathrm{~km}$ , and the trip took $4 \mathrm{hr}$ . At what average rate was Janet traveling?

Solve the problem. -A plane flies 500 miles with the wind and 300 miles against the wind in the same length of time. If the speed of the wind is $23 \mathrm{mph}$ , what is the speed of the plane in still air?

Solve the equation. - $0.08x+0.13(x+1800)=360$

Solve the problem. -Which one of the following inequalities is equivalent to $z \geq-6$ ?

For the compound inequality, give the solution set in both interval and graph forms. - $11 \leq 2 x+5$ and $9 x+5<68$ $For the compound inequality, give the solution set in both interval and graph forms. - 11 \leq 2 x+5 and 9 x+5<68$

Solve the equation or inequality. - $|z-6| \geq 0$

If $k<0$ , what is the solution set of $|3 f+1|< k$

For the compound inequality, give the solution set in both interval and graph forms. - $12 x-8<4 x$ or $-2 x \leq-6$ $For the compound inequality, give the solution set in both interval and graph forms. - 12 x-8<4 x or -2 x \leq-6$

Solve the inequality and graph the solution set. - $|7 y-9|>-8$

For the compound inequality, give the solution set in both interval and graph forms. - $4 x-10 \leq 18$ and $2 x-1 \geq 13$ $For the compound inequality, give the solution set in both interval and graph forms. - 4 x-10 \leq 18 and 2 x-1 \geq 13$

Solve the inequality and graph the solution set. - $|m+1|<0$

Solve the inequality. Give the solution set in both interval and graph forms. - $\frac{4x + 6}{-7} < -\frac{17}{2}$ $Solve the inequality. Give the solution set in both interval and graph forms. - \frac{4x + 6}{-7} < -\frac{17}{2}$

Solve the investment problem. -Walt made an extra $\$ 5000$ last year from a part-time job. He invested part of the money at $10 \%$ and the rest at $8 \%$ . He made a total of $\$ 420$ in interest. How much was invested at $8 \%$ ?

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

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - −15s+130+5(3s−25)=0-15 s+130+5(3 s-25)=0−15s+130+5(3s−25)=0

Use the variable xxx for the unknown, and write an equation representing the verbal sentence. Then solve the problem. -When 50%50 \%50% of a number is subtracted from 70 , the result is 2 less than the number.

Solve the equation. - ∣n−9∣=∣1−n∣|\mathrm{n}-9|=|1-\mathrm{n}|∣n−9∣=∣1−n∣

Solve the problem involving consecutive integers. -The sum of the page numbers on the facing pages of a book is 313 . Find the larger page number.

Solve the equation for the specified variable. Use the distributive property to factor as necessary. - −6k+ar=r−9y-6 k+a r=r-9 y−6k+ar=r−9y for rrr

Let A {q, s, u, v, w, x, y, z}, B {q, s, y, z}, C {v, w, x, y, z}, and D {s}. Specify the following set. - A∪BA \cup BA∪B

Solve the problem. -Janet drove 284 km284 \mathrm{~km}284 km , and the trip took 4hr4 \mathrm{hr}4hr . At what average rate was Janet traveling?

Solve the problem. -A plane flies 500 miles with the wind and 300 miles against the wind in the same length of time. If the speed of the wind is 23mph23 \mathrm{mph}23mph , what is the speed of the plane in still air?

Solve the equation. - 0.08x+0.13(x+1800)=360 0.08x+0.13(x+1800)=3600.08x+0.13(x+1800)=360

Solve the problem. -Which one of the following inequalities is equivalent to z≥−6z \geq-6z≥−6 ?

For the compound inequality, give the solution set in both interval and graph forms. - 11≤2x+511 \leq 2 x+511≤2x+5 and 9x+5<689 x+5<689x+5<68

Solve the equation or inequality. - ∣z−6∣≥0|z-6| \geq 0∣z−6∣≥0

If k<0k<0k<0 , what is the solution set of ∣3f+1∣<k|3 f+1|< k∣3f+1∣<k

For the compound inequality, give the solution set in both interval and graph forms. - 12x−8<4x12 x-8<4 x12x−8<4x or −2x≤−6-2 x \leq-6−2x≤−6

Solve the inequality and graph the solution set. - ∣7y−9∣>−8|7 y-9|>-8∣7y−9∣>−8

For the compound inequality, give the solution set in both interval and graph forms. - 4x−10≤184 x-10 \leq 184x−10≤18 and 2x−1≥132 x-1 \geq 132x−1≥13

Solve the inequality and graph the solution set. - ∣m+1∣<0|m+1|<0∣m+1∣<0

Solve the inequality. Give the solution set in both interval and graph forms. - 4x+6−7<−172\frac{4x + 6}{-7} < -\frac{17}{2}−74x+6​<−217​

Solve the investment problem. -Walt made an extra $5000\$ 5000$5000 last year from a part-time job. He invested part of the money at 10%10 \%10% and the rest at 8%8 \%8% . He made a total of $420\$ 420$420 in interest. How much was invested at 8%8 \%8% ?