Question 1

Graph the solution on a number line, and express it in interval notation.
-$\frac{\mathrm{x}}{-4}<3$

Accepted Answer

A)  $\mathrm{x} \leq-12,(\infty,-12]$
 
B)  $x>-12,(-12, \infty)$
 
C)  $x \geq-12,[-12, \infty)$
 
D)  $\mathrm{x}<-12,(\infty,-12)$

Question 2

The sum of three consecutive odd integers is 207 . Find the integers.

Accepted Answer

A)  $69,71,73$ 
B)  $62,63,64$ 
C)  $71,73,75$ 
D)  $67,69,71$

Question 3

Simplify, where possible
-$5(x-7)$

Accepted Answer

A)  $-35 x$ 
B)  $5 x+35$ 
C)  $5 x-35$ 
D)  $5 \mathrm{x}-7$

Question 4

Solve the inequality. Graph your solution on a number line, and write your solution in interval notation
-$|\mathrm{x}+2|<8$

Accepted Answer

A)  $ (-10, \infty) $
 
B)  $ \varnothing $
 
C)  $ (-10,6) $
 
D)  $ (-\infty, 6) $

Question 5

The density of a substance is its mass per unit volume. A formula that relates a substance's density $\varrho$ (lowercase Greek letter rho) to its mass $\mathrm{m}$ and volume $\mathrm{V}$ is $\mathrm{m}=\varrho \mathrm{V}$. Solve the equation for volume in terms of the other variables.

Accepted Answer

A)  $\varrho=\frac{V}{m}$ 
B)  $V=\frac{m}{\varrho}$ 
C)  $m=\frac{\varrho}{V}$ 
D)  $V=\frac{Q}{m}$

Question 6

Sheila notes that if $\mathrm{a}=20$ and $\mathrm{b}=20$, then $\mathrm{a}-\mathrm{b}=\mathrm{b}-\mathrm{a}=0$. She concludes that for any real numbers $\mathrm{a}$ and $\mathrm{b}, \mathrm{a}-\mathrm{b}=\mathrm{b}-\mathrm{a}$. Do you agree with her reasoning? If not, why not?

Accepted Answer

The answer of Sheila notes that if $\mathrm{a}=20$ and $\mathrm{b}=20$,...

Question 7

Build a variable expression for the given phrase
-A number decreased by two

Accepted Answer

A)  $2-\mathrm{x}$ 
B)  $\frac{x}{2}$ 
C)  $x+2$ 
D)  $x-2$

Question 8

Graph the solution on a number line, and express it in interval notation.
-$-29 \leq-5 x+1<-9$

Accepted Answer

A)  $ -6 \leq x<-2,[-6,-2) $
 
B)  $ 2 \leq x<6,[2,6) $
 
C)  $ 2< x \leq 6,(2,6] $
 
D)  $ -6< x \leq-2,(-6,-2] $

Question 9

A 9- pound puppy is gaining weight at a rate of $\frac{2}{3} \mathrm{lb}$ per week. How much more time will it take for the puppy's weight to exceed $21 \frac{2}{3} \mathrm{lb}$ ?

Accepted Answer

A)  More than $1 \frac{3}{4}$ week(s) 
B)  More than 19 weeks 
C)  More than 46 weeks 
D)  More than 20 weeks

Question 10

Graph the solution on a number line, and express it in interval notation.
-$5 x+11 \leq-25$ or $5 x+11 \geq 25$

Accepted Answer

A)  $-\frac{36}{5} \leq x \leq \frac{14}{5},\left[-\frac{36}{5}, \frac{14}{5}\right]$
 
B)  $\mathrm{x} \leq-\frac{36}{5}$ or $\mathrm{x} \geq \frac{14}{5},\left(-\infty,-\frac{36}{5}\right] \cup\left[\frac{14}{5}, \infty\right)$
 
C)  $\mathrm{x} \leq-8$ or $\mathrm{x} \geq 2,(-\infty,-8] \cup[2, \infty)$
 
D)  $-8 \leq x \leq 2,[-8,2]$

Question 11

$13-5|2+7 \mathrm{x}|=-4$

Accepted Answer

A)  $\left\{\frac{1}{5}\right\}$ 
B)  $\left\{1,-\frac{27}{7}\right\}$ 
C)  $\left\{\frac{3}{7},-\frac{19}{35}\right\}$ 
D)  $\left\{\frac{1}{5},-\frac{27}{35}\right\}$

Question 12

Company A rents copiers for a monthly charge of $\$ 180$ plus 6 cents per copy. Company B rents copiers for a monthly charge of $\$ 360$ plus 3 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

Accepted Answer

A)  6100 copies 
B)  12,000 copies 
C)  6000 copies 
D)  3000 copies

Question 13

$\frac{4 n-2}{9}=\frac{n}{5}$

Accepted Answer

A)  $\left\{\frac{4}{5}\right\}$ 
B)  $\left\{\frac{5}{11}\right\}$ 
C)  $\left\{\frac{11}{10}\right\}$ 
D)  $\left\{\frac{10}{11}\right\}$

Question 14

For the expression,

Accepted Answer

A)  determine the number of terms;
b) write down each term; and
c) write down the coefficient for each.
Be sure to simplify the expression before answering.
-$6 x^{2}-x-9\left(6 x^{2}-4 x+6\right)$ 
A)  a) 3
b) $-48 x^{2},-37 x,-54$
c) $-48,-37,-54$ 
B)  a) 3
b) $-48 x^{2},-5 x, 6$
c) $-48,-5,6$ 
C)  a) 3
b) $-48 x^{2}, 3 x,-6$
c) $-48,3,-6$ 
D)  a) 3
b) $-48 x^{2}, 35 x,-54$
c) $-48,35,-54$

Question 15

$\mathrm{z}-6=1$

Accepted Answer

A)  $\{5\}$ 
B)  $\{5\}$. 
C)  $\{7\}$ 
D)  $\{7\}$.

Question 16

A college charges $\$ 219$ per unit for tuition. If we let $u$ represent the number of units that a student is taking, build a variable expression for the student's tuition.

Accepted Answer

A)  $219 \div \mathrm{u}$ 
B)  $219 u$ 
C)  $u \div 219$ 
D)  $219+u$

Question 17

If $a \leq b$, is it always true that $a^{2} \leq b^{2}$ ? Explain.

Accepted Answer

A) True 
 B)False

Question 18

$|9-8 \mathrm{x}|=6$

Accepted Answer

A)  $\left\{\frac{3}{8}\right\}$ 
B)  $\left\{-\frac{15}{8},-\frac{3}{8}\right\}$ 
C)  $\left\{-\frac{15}{8}\right\}$ 
D)  $\left\{\frac{3}{8}, \frac{15}{8}\right\}$

Question 19

Simplify, where possible
-$21 m-8-4 m-5$

Accepted Answer

A)  $17 \mathrm{~m}-3$ 
B)  $17 m-8 n-5$ 
C)  $17 \mathrm{~m}-13$ 
D)  $-17 m-13$

Question 20

$|\mathrm{x}-7|=0$

Accepted Answer

A)  $\{7,-7\}$ 
B)  $\{7\}$ 
C)  $\{7\}$. 
D)  $\varnothing$

Exam 2: Linear and Absolute Value Equations and Inequalities

The sum of three consecutive odd integers is 207 . Find the integers.

Simplify, where possible - $5(x-7)$

The density of a substance is its mass per unit volume. A formula that relates a substance's density $\varrho$ (lowercase Greek letter rho) to its mass $\mathrm{m}$ and volume $\mathrm{V}$ is $\mathrm{m}=\varrho \mathrm{V}$ . Solve the equation for volume in terms of the other variables.

Sheila notes that if $\mathrm{a}=20$ and $\mathrm{b}=20$ , then $\mathrm{a}-\mathrm{b}=\mathrm{b}-\mathrm{a}=0$ . She concludes that for any real numbers $\mathrm{a}$ and $\mathrm{b}, \mathrm{a}-\mathrm{b}=\mathrm{b}-\mathrm{a}$ . Do you agree with her reasoning? If not, why not?

Build a variable expression for the given phrase -A number decreased by two

Graph the solution on a number line, and express it in interval notation. - $-29 \leq-5 x+1<-9$ $Graph the solution on a number line, and express it in interval notation. - -29 \leq-5 x+1<-9 A) -6 \leq x<-2,[-6,-2) B) 2 \leq x<6,[2,6) C) 2< x \leq 6,(2,6] D) -6< x \leq-2,(-6,-2]$

A 9- pound puppy is gaining weight at a rate of $\frac{2}{3} \mathrm{lb}$ per week. How much more time will it take for the puppy's weight to exceed $21 \frac{2}{3} \mathrm{lb}$ ?

$13-5|2+7 \mathrm{x}|=-4$

Company A rents copiers for a monthly charge of $\$ 180$ plus 6 cents per copy. Company B rents copiers for a monthly charge of $\$ 360$ plus 3 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

$\frac{4 n-2}{9}=\frac{n}{5}$

For the expression, A) determine the number of terms; b) write down each term; and c) write down the coefficient for each. Be sure to simplify the expression before answering. - $6 x^{2}-x-9\left(6 x^{2}-4 x+6\right)$

$\mathrm{z}-6=1$

A college charges $\$ 219$ per unit for tuition. If we let $u$ represent the number of units that a student is taking, build a variable expression for the student's tuition.

If $a \leq b$ , is it always true that $a^{2} \leq b^{2}$ ? Explain.

$|9-8 \mathrm{x}|=6$

Simplify, where possible - $21 m-8-4 m-5$

$|\mathrm{x}-7|=0$

Exam 2: Linear and Absolute Value Equations and Inequalities

Graph the solution on a number line, and express it in interval notation. - x−4<3\frac{\mathrm{x}}{-4}<3−4x​<3

The sum of three consecutive odd integers is 207 . Find the integers.

Simplify, where possible - 5(x−7) 5(x-7) 5(x−7)

Solve the inequality. Graph your solution on a number line, and write your solution in interval notation - ∣x+2∣<8|\mathrm{x}+2|<8∣x+2∣<8

The density of a substance is its mass per unit volume. A formula that relates a substance's density ϱ\varrhoϱ (lowercase Greek letter rho) to its mass m\mathrm{m}m and volume V\mathrm{V}V is m=ϱV\mathrm{m}=\varrho \mathrm{V}m=ϱV . Solve the equation for volume in terms of the other variables.

Build a variable expression for the given phrase -A number decreased by two

Graph the solution on a number line, and express it in interval notation. - −29≤−5x+1<−9-29 \leq-5 x+1<-9−29≤−5x+1<−9

A 9- pound puppy is gaining weight at a rate of 23lb\frac{2}{3} \mathrm{lb}32​lb per week. How much more time will it take for the puppy's weight to exceed 2123lb21 \frac{2}{3} \mathrm{lb}2132​lb ?

Graph the solution on a number line, and express it in interval notation. - 5x+11≤−255 x+11 \leq-255x+11≤−25 or 5x+11≥255 x+11 \geq 255x+11≥25

13−5∣2+7x∣=−413-5|2+7 \mathrm{x}|=-413−5∣2+7x∣=−4

Company A rents copiers for a monthly charge of $180\$ 180$180 plus 6 cents per copy. Company B rents copiers for a monthly charge of $360\$ 360$360 plus 3 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

4n−29=n5\frac{4 n-2}{9}=\frac{n}{5}94n−2​=5n​

For the expression, A) determine the number of terms; b) write down each term; and c) write down the coefficient for each. Be sure to simplify the expression before answering. - 6x2−x−9(6x2−4x+6) 6 x^{2}-x-9\left(6 x^{2}-4 x+6\right) 6x2−x−9(6x2−4x+6)

z−6=1\mathrm{z}-6=1z−6=1

A college charges $219\$ 219$219 per unit for tuition. If we let uuu represent the number of units that a student is taking, build a variable expression for the student's tuition.

If a≤ba \leq ba≤b , is it always true that a2≤b2a^{2} \leq b^{2}a2≤b2 ? Explain.

∣9−8x∣=6|9-8 \mathrm{x}|=6∣9−8x∣=6

Simplify, where possible - 21m−8−4m−521 m-8-4 m-521m−8−4m−5

∣x−7∣=0|\mathrm{x}-7|=0∣x−7∣=0

Simplify, where possible - $5(x-7)$

The density of a substance is its mass per unit volume. A formula that relates a substance's density $\varrho$ (lowercase Greek letter rho) to its mass $\mathrm{m}$ and volume $\mathrm{V}$ is $\mathrm{m}=\varrho \mathrm{V}$ . Solve the equation for volume in terms of the other variables.

Graph the solution on a number line, and express it in interval notation. - $-29 \leq-5 x+1<-9$ $Graph the solution on a number line, and express it in interval notation. - -29 \leq-5 x+1<-9 A) -6 \leq x<-2,[-6,-2) B) 2 \leq x<6,[2,6) C) 2< x \leq 6,(2,6] D) -6< x \leq-2,(-6,-2]$

A 9- pound puppy is gaining weight at a rate of $\frac{2}{3} \mathrm{lb}$ per week. How much more time will it take for the puppy's weight to exceed $21 \frac{2}{3} \mathrm{lb}$ ?

$13-5|2+7 \mathrm{x}|=-4$

Company A rents copiers for a monthly charge of $\$ 180$ plus 6 cents per copy. Company B rents copiers for a monthly charge of $\$ 360$ plus 3 cents per copy. What is the number of copies above which Company A's charges are the higher of the two?

$\frac{4 n-2}{9}=\frac{n}{5}$

For the expression, A) determine the number of terms; b) write down each term; and c) write down the coefficient for each. Be sure to simplify the expression before answering. - $6 x^{2}-x-9\left(6 x^{2}-4 x+6\right)$

$\mathrm{z}-6=1$

A college charges $\$ 219$ per unit for tuition. If we let $u$ represent the number of units that a student is taking, build a variable expression for the student's tuition.

If $a \leq b$ , is it always true that $a^{2} \leq b^{2}$ ? Explain.

$|9-8 \mathrm{x}|=6$

Simplify, where possible - $21 m-8-4 m-5$

$|\mathrm{x}-7|=0$