Question 1

Solve the inequality. Write the solution set in interval notation and graph the solution set.
-$x + 3 < 1$

Accepted Answer

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

Question 2

Solve the equation.
-5(x+5)=(5 x+25)

Accepted Answer

A)  {50} 
B)   { $\{ x \mid x$ is a real number } 
C)   {0} 
D)  $\varnothing$ 
A)  {50} 
B)   { $\{ x \mid x$ is a real number } 
C)   {0} 
D)  $\varnothing$

Question 3

Solve.
-You have a cylindrical cooking pot whose radius is 6 inches and whose height is 7 inches. How many full cans of soup will fit into the pot if each can has holds 10 cubic inches of soup? (Use 3.14 as an approximation for .)

Accepted Answer

A)  79 cans of soup 
B)  80 cans of soup 
C)  26 cans of soup 
D)  25 cans of soup 
A)  79 cans of soup 
B)  80 cans of soup 
C)  26 cans of soup 
D)  25 cans of soup

Question 4

Solve.
-Seven times some number added to 8 amounts to  -10  added to the product of 4 and the number.

Accepted Answer

A)  18 
B)   -18 
C)   -6 
D)  6 
A)  18 
B)   -18 
C)   -6 
D)  6

Question 5

Solve the equation.
-$\frac { 2 x - 1 } { 6 } + x = \frac { 2 x + 1 } { 2 } + 4$

Accepted Answer

A)  $\{ 14 \}$ 
B)   {6} 
C)  $\{ - 13 \}$ 
D)  $\left\{ - \frac { 8 } { 3 } \right\}$ 
A)  $\{ 14 \}$ 
B)   {6} 
C)  $\{ - 13 \}$ 
D)  $\left\{ - \frac { 8 } { 3 } \right\}$

Question 6

Solve the equation for the specified variable.
-$\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ for h

Accepted Answer

A)  $h = \frac { b } { 2 A }$ 
B)  $h = \frac { A b } { 2 }$ 
C)  $h = \frac { A } { 2 b }$ 
D)  $h = \frac { 2 \mathrm {~A} } { \mathrm {~b} }$ 
A)  $h = \frac { b } { 2 A }$ 
B)  $h = \frac { A b } { 2 }$ 
C)  $h = \frac { A } { 2 b }$ 
D)  $h = \frac { 2 \mathrm {~A} } { \mathrm {~b} }$

Question 7

List the elements of the set.
-If  A={  $X \mid X$ is an odd integer  }  and  B={21,23,24,26} , list the elements of $A \cap B$

Accepted Answer

A)  {$\mathrm { X } \mid \mathrm { X }$ is an odd integer} 
B)  $\phi$ 
C)  {$x \mid x$ is an odd integer or  x=24  or  x=26} 
D)   {21,23} 
A)  {$\mathrm { X } \mid \mathrm { X }$ is an odd integer} 
B)  $\phi$ 
C)  {$x \mid x$ is an odd integer or  x=24  or  x=26} 
D)   {21,23}

Question 8

Solve the equation.
-3(x+4)+5=3 x+2

Accepted Answer

A)   {  $x \mid x$ is a real number } 
B)   {11} 
C)   $\varnothing$ 
D)   {15} 
A)   {  $x \mid x$ is a real number } 
B)   {11} 
C)   $\varnothing$ 
D)   {15}

Question 9

Solve the inequality. Write the solution set in interval notation and graph the solution set.
-$3 x + 1 \geq 2 x + 1$

Accepted Answer

A)  $( 2 , \infty )$
  
B)  $( - \infty , 1 ]$
  
C)  $[ 0 , \infty )$
  
D)  $[ - 2 , \infty )$
  
A)  $( 2 , \infty )$
  
B)  $( - \infty , 1 ]$
  
C)  $[ 0 , \infty )$
  
D)  $[ - 2 , \infty )$

Question 10

Solve the equation.
- -(2 x-5)-(3 x-6)+5=-5(x-1)-(2 x+1)+2

Accepted Answer

A)   {5} 
B)   {11} 
C)  $\left\{ - \frac { 5 } { 0 } \right\}$ 
D)   {-5} 
A)   {5} 
B)   {11} 
C)  $\left\{ - \frac { 5 } { 0 } \right\}$ 
D)   {-5}

Question 11

Solve the inequality. Write the answer in interval notation.
-$- 5 \leq \frac { 2 x - 1 } { 3 } < 2$

Accepted Answer

A)  $( - \infty , - 7 ] \cup [ 4 , \infty )$ 
B)  $\left[ - \frac { 13 } { 2 } , 4 \right]$ 
C)  $\left[ - 7 , \frac { 7 } { 2 } \right)$ 
D)  $\left[ - 8 , \frac { 5 } { 2 } \right)$ 
A)  $( - \infty , - 7 ] \cup [ 4 , \infty )$ 
B)  $\left[ - \frac { 13 } { 2 } , 4 \right]$ 
C)  $\left[ - 7 , \frac { 7 } { 2 } \right)$ 
D)  $\left[ - 8 , \frac { 5 } { 2 } \right)$

Question 12

Solve the equation for the specified variable.
-$\mathrm { V } = \frac { 1 } { 3 } \mathrm { Ah }$ for h

Accepted Answer

A)  $h = \frac { V } { 3 A }$ 
B)  $h = \frac { 3 \mathrm {~A} } { \mathrm {~V} }$ 
C)  $h = \frac { 3 V } { A }$ 
D)  $h = \frac { A } { 3 V }$ 
A)  $h = \frac { V } { 3 A }$ 
B)  $h = \frac { 3 \mathrm {~A} } { \mathrm {~V} }$ 
C)  $h = \frac { 3 V } { A }$ 
D)  $h = \frac { A } { 3 V }$

Question 13

Solve.
-You are varnishing the background for a rectangular mural. The base of the mural is 7$\frac { 1 } { 2 }$meters and the height of the mural is 3 meters. How many cans of varnish will you need if each can covers 10 square meters?

Accepted Answer

A)  23 cans of varnish 
B)  5 cans of varnish 
C)  3 cans of varnish 
D)  9 cans of varnish 
A)  23 cans of varnish 
B)  5 cans of varnish 
C)  3 cans of varnish 
D)  9 cans of varnish

Question 14

Solve.
-$| x | = 6$

Accepted Answer

A)   {-6} 
B)   {36} 
C)   {6,-6} 
D)   {6} 
A)   {-6} 
B)   {36} 
C)   {6,-6} 
D)   {6}

Question 15

Solve the equation.
- 4(x+7)=5(x-3)

Accepted Answer

A)   {43} 
B)   {13} 
C)  {$x \mid x$ is a real number} 
D)  $\{ \varnothing \}$ 
A)   {43} 
B)   {13} 
C)  {$x \mid x$ is a real number} 
D)  $\{ \varnothing \}$

Question 16

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { contradiction } & \text { linear inequality in one variable compound inequalitysolution } \
\text { absolute value } & \text { consecutive integers union } \
\text { formula } & \text { linear equation in one variable intersection }
\end{array}$$
-The _____ of two sets is the set of all elements that belong to either of the sets.

Accepted Answer

A)  absolute value 
B)  intersection 
C)  solution 
D)  union 
A)  absolute value 
B)  intersection 
C)  solution 
D)  union

Question 17

Solve the equation.
-9 x=5(5 x+3)

Accepted Answer

A)  $\left\{ \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 15 } { 16 } \right\}$ 
C)  $\left\{ \frac { 16 } { 15 } \right\}$ 
D)  $\left\{ \frac { 15 } { 16 } \right\}$ 
A)  $\left\{ \frac { 5 } { 3 } \right\}$ 
B)  $\left\{ - \frac { 15 } { 16 } \right\}$ 
C)  $\left\{ \frac { 16 } { 15 } \right\}$ 
D)  $\left\{ \frac { 15 } { 16 } \right\}$

Question 18

List the elements of the set.
-If  A={7,8,9,12}  and  B={5,7,8,10} , list the elements of $\mathrm { A } \cap \mathrm { B }$

Accepted Answer

A)   {5,7,8,9,10,12} 
B)   {7,8} 
C)   {5,9,10,12} 
D)   $\phi$ 
A)   {5,7,8,9,10,12} 
B)   {7,8} 
C)   {5,9,10,12} 
D)   $\phi$

Question 19

Solve the compound inequality. Give the answer in interval notation.
-$4 x - 2 > 2 \text { or } - x + 4 \geq - 9$

Accepted Answer

A)  $( - \infty , 1 ] \cup ( 13 , \infty )$ 
B)  $( 1 , \infty )$ 
C)  $( - \infty , 1 ) \cup [ 13 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $( - \infty , 1 ] \cup ( 13 , \infty )$ 
B)  $( 1 , \infty )$ 
C)  $( - \infty , 1 ) \cup [ 13 , \infty )$ 
D)  $( - \infty , \infty )$

Question 20

Solve the equation.
-$\frac { x } { 5 } = \frac { x } { 3 } + \frac { 9 } { 5 }$

Accepted Answer

A)  $\left\{ - \frac { 2 } { 27 } \right\}$ 
B)   {0} 
C)  $\left\{ - \frac { 9 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 27 } { 2 } \right\}$ 
A)  $\left\{ - \frac { 2 } { 27 } \right\}$ 
B)   {0} 
C)  $\left\{ - \frac { 9 } { 5 } \right\}$ 
D)  $\left\{ - \frac { 27 } { 2 } \right\}$

Solve the inequality. Write the solution set in interval notation and graph the solution set. - $x + 3 < 1$

Solve the equation. -5(x+5)=(5 x+25)

Solve. -You have a cylindrical cooking pot whose radius is 6 inches and whose height is 7 inches. How many full cans of soup will fit into the pot if each can has holds 10 cubic inches of soup? (Use 3.14 as an approximation for .)

Solve. -Seven times some number added to 8 amounts to -10 added to the product of 4 and the number.

Solve the equation. - $\frac { 2 x - 1 } { 6 } + x = \frac { 2 x + 1 } { 2 } + 4$

Solve the equation for the specified variable. - $\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ for h

List the elements of the set. -If A={ $X \mid X$ is an odd integer } and B={21,23,24,26} , list the elements of $A \cap B$

Solve the equation. -3(x+4)+5=3 x+2

Solve the inequality. Write the solution set in interval notation and graph the solution set. - $3 x + 1 \geq 2 x + 1$ $Solve the inequality. Write the solution set in interval notation and graph the solution set. - 3 x + 1 \geq 2 x + 1$

Solve the equation. - -(2 x-5)-(3 x-6)+5=-5(x-1)-(2 x+1)+2

Solve the inequality. Write the answer in interval notation. - $- 5 \leq \frac { 2 x - 1 } { 3 } < 2$

Solve the equation for the specified variable. - $\mathrm { V } = \frac { 1 } { 3 } \mathrm { Ah }$ for h

Solve. -You are varnishing the background for a rectangular mural. The base of the mural is 7 $\frac { 1 } { 2 }$ meters and the height of the mural is 3 meters. How many cans of varnish will you need if each can covers 10 square meters?

Solve. - $| x | = 6$

Solve the equation. - 4(x+7)=5(x-3)

Solve the equation. -9 x=5(5 x+3)

List the elements of the set. -If A={7,8,9,12} and B={5,7,8,10} , list the elements of $\mathrm { A } \cap \mathrm { B }$

Solve the compound inequality. Give the answer in interval notation. - $4 x - 2 > 2 \text { or } - x + 4 \geq - 9$

Solve the equation. - $\frac { x } { 5 } = \frac { x } { 3 } + \frac { 9 } { 5 }$

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Exam 2: Equations, Inequalities, and Problem Solving

Solve the inequality. Write the solution set in interval notation and graph the solution set. - x+3<1x + 3 < 1x+3<1