Question 1

When solving a "word problem" we set up an equation in $x$. Give an example where the solution of the equation is not the answer to the problem.

Accepted Answer

Answers will vary. An example would be:

Question 2

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
-9 times a number

Accepted Answer

A)  $9+x$ 
B)  $9 x$ 
C)  $9-x$ 
D)  $\frac{9}{x}$ 
A)  $9+x$ 
B)  $9 x$ 
C)  $9-x$ 
D)  $\frac{9}{x}$

Question 3

For the compound inequality, give the solution set in both interval and graph forms.
-$6 x-8 \geq-38$ and $6 x-8 \leq-14$

Accepted Answer

A)  $[-5,-1)$
  
B)  $(-5,-1]$
  
C)  $[-5,-1]$
  
D)  $(-5,-1)$
  
A)  $[-5,-1)$
  
B)  $(-5,-1]$
  
C)  $[-5,-1]$
  
D)  $(-5,-1)$

Question 4

Suppose the formula $s=\frac{1}{2} \mathrm{gt}^{2}+\mathrm{v}_{\mathrm{O}} \mathrm{t}$ is solved for $\mathrm{t}$ with the following result: $\mathrm{t}=\frac{2 \mathrm{~s}}{\mathrm{gt}+2 \mathrm{v}_{\mathrm{O}}}$. Is this an acceptable solution? Explain.

Accepted Answer

No. The variable t s

Question 5

Solve the inequality. Give the solution set in both interval and graph forms.
-$-2 z+9 \leq-3 z+13$

Accepted Answer

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

Question 6

Solve the problem.
-Jill is 22 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at $2.5 \mathrm{~km} / \mathrm{hr}$. They meet in 4 hours. How fast is Joe walking?

Accepted Answer

A)  $3 \mathrm{~km} / \mathrm{hr}$ 
B)  $8 \mathrm{~km} / \mathrm{hr}$ 
C)  $12 \mathrm{~km} / \mathrm{hr}$ 
D)  $2.75 \mathrm{~km} / \mathrm{hr}$ 
A)  $3 \mathrm{~km} / \mathrm{hr}$ 
B)  $8 \mathrm{~km} / \mathrm{hr}$ 
C)  $12 \mathrm{~km} / \mathrm{hr}$ 
D)  $2.75 \mathrm{~km} / \mathrm{hr}$

Question 7

Solve the percent problem.
-At the end of the day, a storekeeper had $\$ 1248$ in the cash register, counting both the sale of goods and the sales tax of $4 \%$. Find the amount that is the tax.

Accepted Answer

A)  $\$ 43$ 
B)  $\$ 53$ 
C)  $\$ 38$ 
D)  $\$ 48$ 
A)  $\$ 43$ 
B)  $\$ 53$ 
C)  $\$ 38$ 
D)  $\$ 48$

Question 8

Solve the equation.
-$14(3 c-6)=9 c-3$

Accepted Answer

A)  $\left\{\frac{27}{11}\right\}$ 
B)  $\left\{-\frac{27}{11}\right\}$ 
C)  $\left\{\frac{87}{11}\right\}$ 
D)  $\left\{\frac{9}{17}\right\}$ 
A)  $\left\{\frac{27}{11}\right\}$ 
B)  $\left\{-\frac{27}{11}\right\}$ 
C)  $\left\{\frac{87}{11}\right\}$ 
D)  $\left\{\frac{9}{17}\right\}$

Question 9

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set.
-$4(4 g+17)-16 g-68=0$

Accepted Answer

A)  Conditional; $\{4\}$ 
B)  Identity; {all real numbers} 
C)  Conditional; $\{0\}$ 
D)  Contradiction; $\varnothing$ 
A)  Conditional; $\{4\}$ 
B)  Identity; {all real numbers} 
C)  Conditional; $\{0\}$ 
D)  Contradiction; $\varnothing$

Question 10

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number.
-The product of 6 more than a number and 1 less than the number

Accepted Answer

A)  $(x+6)(x-1)$ 
B)  $x+6(x-1)$ 
C)  $(x+6)(1-x)$ 
D)  $(x+6)-1$ 
A)  $(x+6)(x-1)$ 
B)  $x+6(x-1)$ 
C)  $(x+6)(1-x)$ 
D)  $(x+6)-1$

Question 11

Express the set in the simplest interval form.
-$(-\infty, 4) \cap(-1, \infty)$

Accepted Answer

A)  $(-1,4)$ 
B)  $(-\infty, \infty)$ 
C)  $[-1,4)$ 
D)  $(-\infty,-1]$ 
A)  $(-1,4)$ 
B)  $(-\infty, \infty)$ 
C)  $[-1,4)$ 
D)  $(-\infty,-1]$

Question 12

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.
-$\mathrm{C} \cap \mathrm{D}$

Accepted Answer

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

Question 13

Solve the problem involving consecutive integers.
-The sum of three consecutive even integers is 156 . Find the integers.

Accepted Answer

A)  $50,52,54$ 
B)  $54,56,58$ 
C)  $45,46,47$ 
D)  $52,54,56$ 
A)  $50,52,54$ 
B)  $54,56,58$ 
C)  $45,46,47$ 
D)  $52,54,56$

Question 14

Solve the problem.
-Find the measures of the complementary angles.

Accepted Answer

A)  $150^{\circ}, 30^{\circ}$ 
B)  $75^{\circ}, 15^{\circ}$ 
C)  $70^{\circ}, 20^{\circ}$ 
D)  $37.5^{\circ}, 7.5^{\circ}$ 
A)  $150^{\circ}, 30^{\circ}$ 
B)  $75^{\circ}, 15^{\circ}$ 
C)  $70^{\circ}, 20^{\circ}$ 
D)  $37.5^{\circ}, 7.5^{\circ}$

Question 15

Which of the following is not a correct answer when the formula $A=\frac{1}{2} h(b+B)$ is solved for $b$ ?

Accepted Answer

A)  $\frac{2 \mathrm{~A}-\mathrm{B}}{\mathrm{h}}$ 
B)  $\frac{2 \mathrm{~A}-\mathrm{Bh}}{\mathrm{h}}$ 
C)  $\frac{2 \mathrm{~A}}{\mathrm{~h}}-\mathrm{B}$ 
D)  $ \frac{A-\frac{1}{2} B h}{\frac{1}{2} h} $ 
A)  $\frac{2 \mathrm{~A}-\mathrm{B}}{\mathrm{h}}$ 
B)  $\frac{2 \mathrm{~A}-\mathrm{Bh}}{\mathrm{h}}$ 
C)  $\frac{2 \mathrm{~A}}{\mathrm{~h}}-\mathrm{B}$ 
D)  $ \frac{A-\frac{1}{2} B h}{\frac{1}{2} h} $

Question 16

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.
-$|8 k+2|+7<16$

Accepted Answer

A)  $\varnothing$ 
B)  $\left(-\infty,-\frac{11}{8}\right) \cup\left(\frac{7}{8}, \infty\right)$ 
C)  $\left(-\infty,-\frac{11}{8}\right)$ 
D)  $\left(-\frac{11}{8}, \frac{7}{8}\right)$ 
A)  $\varnothing$ 
B)  $\left(-\infty,-\frac{11}{8}\right) \cup\left(\frac{7}{8}, \infty\right)$ 
C)  $\left(-\infty,-\frac{11}{8}\right)$ 
D)  $\left(-\frac{11}{8}, \frac{7}{8}\right)$

Question 17

Decide whether the following is an expression or an equation. Simplify any expression or solve any equation.
-$\frac{1}{7} x+\frac{1}{2} x-\frac{1}{5}+5$

Accepted Answer

A)  Expression; $\frac{5}{14} x+\frac{26}{5}$ 
B)  Equation; $\left\{\frac{364}{45}\right\}$ 
C)  Equation; $\left\{-\frac{112}{15}\right\}$ 
D)  Expression; $\frac{9}{14} x+\frac{24}{5}$ 
A)  Expression; $\frac{5}{14} x+\frac{26}{5}$ 
B)  Equation; $\left\{\frac{364}{45}\right\}$ 
C)  Equation; $\left\{-\frac{112}{15}\right\}$ 
D)  Expression; $\frac{9}{14} x+\frac{24}{5}$

Question 18

Solve the problem.
-The graph shows the percent of students at a local high school who were enrolled in a foreign language class each school year during the 1980s.
 
What is the best estimate for the number of students taking a language in 1982 if a total of 2630 students were enrolled in the school?

Accepted Answer

A)  2233 students 
B)  66 students 
C)  2183 students 
D)  447 students 
A)  2233 students 
B)  66 students 
C)  2183 students 
D)  447 students

Question 19

Solve the inequality and graph the solution set.
-$|3 x-4| \geq 5$

Accepted Answer

A)  $\left[-\frac{1}{3}, 3\right]$
  
B)  $(-\infty,-3] \cup\left[\frac{1}{3}, \infty\right)$
  
C)  $[3, \infty)$,
  
D)  $\left(-\infty,-\frac{1}{3}\right] \cup[3, \infty )$
  
A)  $\left[-\frac{1}{3}, 3\right]$
  
B)  $(-\infty,-3] \cup\left[\frac{1}{3}, \infty\right)$
  
C)  $[3, \infty)$,
  
D)  $\left(-\infty,-\frac{1}{3}\right] \cup[3, \infty )$

Question 20

If $a  \frac{1}{b}$ ? Explain.

Accepted Answer

No. The second statement only follows fr

When solving a "word problem" we set up an equation in $x$ . Give an example where the solution of the equation is not the answer to the problem.

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -9 times a number

For the compound inequality, give the solution set in both interval and graph forms. - $6 x-8 \geq-38$ and $6 x-8 \leq-14$ $For the compound inequality, give the solution set in both interval and graph forms. - 6 x-8 \geq-38 and 6 x-8 \leq-14$

Suppose the formula $s=\frac{1}{2} \mathrm{gt}^{2}+\mathrm{v}_{\mathrm{O}} \mathrm{t}$ is solved for $\mathrm{t}$ with the following result: $\mathrm{t}=\frac{2 \mathrm{~s}}{\mathrm{gt}+2 \mathrm{v}_{\mathrm{O}}}$ . Is this an acceptable solution? Explain.

Solve the inequality. Give the solution set in both interval and graph forms. - $-2 z+9 \leq-3 z+13$ $Solve the inequality. Give the solution set in both interval and graph forms. - -2 z+9 \leq-3 z+13$

Solve the problem. -Jill is 22 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at $2.5 \mathrm{~km} / \mathrm{hr}$ . They meet in 4 hours. How fast is Joe walking?

Solve the percent problem. -At the end of the day, a storekeeper had $\$ 1248$ in the cash register, counting both the sale of goods and the sales tax of $4 \%$ . Find the amount that is the tax.

Solve the equation. - $14(3 c-6)=9 c-3$

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $4(4 g+17)-16 g-68=0$

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -The product of 6 more than a number and 1 less than the number

Express the set in the simplest interval form. - $(-\infty, 4) \cap(-1, \infty)$

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. - $\mathrm{C} \cap \mathrm{D}$

Solve the problem involving consecutive integers. -The sum of three consecutive even integers is 156 . Find the integers.

Solve the problem. -Find the measures of the complementary angles.

Which of the following is not a correct answer when the formula $A=\frac{1}{2} h(b+B)$ is solved for $b$ ?

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. - $|8 k+2|+7<16$

Decide whether the following is an expression or an equation. Simplify any expression or solve any equation. - $\frac{1}{7} x+\frac{1}{2} x-\frac{1}{5}+5$

Solve the problem. -The graph shows the percent of students at a local high school who were enrolled in a foreign language class each school year during the 1980s. What is the best estimate for the number of students taking a language in 1982 if a total of 2630 students were enrolled in the school?

Solve the inequality and graph the solution set. - $|3 x-4| \geq 5$ $Solve the inequality and graph the solution set. - |3 x-4| \geq 5$

If $a < b$ , is it always true that $\frac{1}{a} > \frac{1}{b}$ ? Explain.

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

When solving a "word problem" we set up an equation in xxx . Give an example where the solution of the equation is not the answer to the problem.

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -9 times a number

For the compound inequality, give the solution set in both interval and graph forms. - 6x−8≥−386 x-8 \geq-386x−8≥−38 and 6x−8≤−146 x-8 \leq-146x−8≤−14

Solve the inequality. Give the solution set in both interval and graph forms. - −2z+9≤−3z+13-2 z+9 \leq-3 z+13−2z+9≤−3z+13

Solve the problem. -Jill is 22 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at 2.5 km/hr2.5 \mathrm{~km} / \mathrm{hr}2.5 km/hr . They meet in 4 hours. How fast is Joe walking?

Solve the percent problem. -At the end of the day, a storekeeper had $1248\$ 1248$1248 in the cash register, counting both the sale of goods and the sales tax of 4%4 \%4% . Find the amount that is the tax.

Solve the equation. - 14(3c−6)=9c−314(3 c-6)=9 c-314(3c−6)=9c−3

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - 4(4g+17)−16g−68=04(4 g+17)-16 g-68=04(4g+17)−16g−68=0

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -The product of 6 more than a number and 1 less than the number

Express the set in the simplest interval form. - (−∞,4)∩(−1,∞)(-\infty, 4) \cap(-1, \infty)(−∞,4)∩(−1,∞)

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. - C∩D\mathrm{C} \cap \mathrm{D}C∩D

Solve the problem involving consecutive integers. -The sum of three consecutive even integers is 156 . Find the integers.

Solve the problem. -Find the measures of the complementary angles.

Which of the following is not a correct answer when the formula A=12h(b+B)A=\frac{1}{2} h(b+B)A=21​h(b+B) is solved for bbb ?

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. - ∣8k+2∣+7<16|8 k+2|+7<16∣8k+2∣+7<16

Decide whether the following is an expression or an equation. Simplify any expression or solve any equation. - 17x+12x−15+5\frac{1}{7} x+\frac{1}{2} x-\frac{1}{5}+571​x+21​x−51​+5

Solve the problem. -The graph shows the percent of students at a local high school who were enrolled in a foreign language class each school year during the 1980s. What is the best estimate for the number of students taking a language in 1982 if a total of 2630 students were enrolled in the school?

Solve the inequality and graph the solution set. - ∣3x−4∣≥5|3 x-4| \geq 5∣3x−4∣≥5

If a<ba < ba<b , is it always true that 1a>1b\frac{1}{a} > \frac{1}{b}a1​>b1​ ? Explain.

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

When solving a "word problem" we set up an equation in $x$ . Give an example where the solution of the equation is not the answer to the problem.

For the compound inequality, give the solution set in both interval and graph forms. - $6 x-8 \geq-38$ and $6 x-8 \leq-14$ $For the compound inequality, give the solution set in both interval and graph forms. - 6 x-8 \geq-38 and 6 x-8 \leq-14$

Solve the inequality. Give the solution set in both interval and graph forms. - $-2 z+9 \leq-3 z+13$ $Solve the inequality. Give the solution set in both interval and graph forms. - -2 z+9 \leq-3 z+13$

Solve the problem. -Jill is 22 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks at $2.5 \mathrm{~km} / \mathrm{hr}$ . They meet in 4 hours. How fast is Joe walking?

Solve the percent problem. -At the end of the day, a storekeeper had $\$ 1248$ in the cash register, counting both the sale of goods and the sales tax of $4 \%$ . Find the amount that is the tax.

Solve the equation. - $14(3 c-6)=9 c-3$

Decide whether the equation is conditional, an identity, or a contradiction. Give the solution set. - $4(4 g+17)-16 g-68=0$

Express the set in the simplest interval form. - $(-\infty, 4) \cap(-1, \infty)$

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. - $\mathrm{C} \cap \mathrm{D}$

Which of the following is not a correct answer when the formula $A=\frac{1}{2} h(b+B)$ is solved for $b$ ?

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. - $|8 k+2|+7<16$

Decide whether the following is an expression or an equation. Simplify any expression or solve any equation. - $\frac{1}{7} x+\frac{1}{2} x-\frac{1}{5}+5$

Solve the inequality and graph the solution set. - $|3 x-4| \geq 5$ $Solve the inequality and graph the solution set. - |3 x-4| \geq 5$

If $a < b$ , is it always true that $\frac{1}{a} > \frac{1}{b}$ ? Explain.