Algebra, NAPX-J4-CA36 SA

Question

{{{question}}}

Worked Solution

{{{workedSolution}}}

Variant 0

DifficultyLevel

731

Question

In this inequality n\large n is a whole number.

5n<35\dfrac{5}{\large n} < \dfrac{3}{5}


What is the smallest possible value for n\large n to make this inequality true?

Worked Solution
5n\dfrac{5}{\large n} < 35\dfrac{3}{5}
3n3\large n > 25
n\large n > 253\dfrac{25}{3}
n\large n > 8.33...

∴\therefore Smallest  n\ \large n = 9

Question Type

Answer Box

Variables

Variable nameVariable value
question
In this inequality $\large n$ is a whole number. >$\dfrac{5}{\large n} < \dfrac{3}{5}$
What is the smallest possible value for $\large n$ to make this inequality true?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{5}{\large n}$ | < $\dfrac{3}{5}$ | | $3\large n$ | > 25 | | $\large n$ | > $\dfrac{25}{3}$ | | $\large n$ | > 8.33... |

$\therefore$ Smallest $\ \large n$ = {{{correctAnswer0}}}
correctAnswer0
9
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer09

Variant 1

DifficultyLevel

731

Question

In this inequality x\large x is a whole number.

7x<43\dfrac{7}{\large x} < \dfrac{4}{3}


What is the smallest possible value for x\large x to make this inequality true?

Worked Solution
7x\dfrac{7}{\large x} < 43\dfrac{4}{3}
4x4\large x > 21
x\large x > 214\dfrac{21}{4}
x\large x > 5.25

∴\therefore Smallest  x\ \large x = 6

Question Type

Answer Box

Variables

Variable nameVariable value
question
In this inequality $\large x$ is a whole number. >$\dfrac{7}{\large x} < \dfrac{4}{3}$
What is the smallest possible value for $\large x$ to make this inequality true?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{7}{\large x}$ | < $\dfrac{4}{3}$ | | $4\large x$ | > 21 | | $\large x$ | > $\dfrac{21}{4}$ | | $\large x$ | > 5.25 |

$\therefore$ Smallest $\ \large x$ = {{{correctAnswer0}}}
correctAnswer0
6
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer06

Variant 2

DifficultyLevel

729

Question

In this inequality n\large n is a whole number.

9n<74\dfrac{9}{\large n} < \dfrac{7}{4}


What is the smallest possible value for n\large n to make this inequality true?

Worked Solution
9n\dfrac{9}{\large n} < 74\dfrac{7}{4}
7n7\large n > 36
n\large n > 367\dfrac{36}{7}
n\large n > 5.142...

∴\therefore Smallest  n\ \large n = 6

Question Type

Answer Box

Variables

Variable nameVariable value
question
In this inequality $\large n$ is a whole number. >$\dfrac{9}{\large n} < \dfrac{7}{4}$
What is the smallest possible value for $\large n$ to make this inequality true?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{9}{\large n}$ | < $\dfrac{7}{4}$ | | $7\large n$ | > 36 | | $\large n$ | > $\dfrac{36}{7}$ | | $\large n$ | > 5.142... |

$\therefore$ Smallest $\ \large n$ = {{{correctAnswer0}}}
correctAnswer0
6
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer06

Variant 3

DifficultyLevel

735

Question

In this inequality m\large m is a whole number.

11m<34\dfrac{11}{\large m} < \dfrac{3}{4}


What is the smallest possible value for m\large m to make this inequality true?

Worked Solution
11m\dfrac{11}{\large m} < 34\dfrac{3}{4}
3m3\large m > 44
m\large m > 443\dfrac{44}{3}
m\large m > 14.66...

∴\therefore Smallest  m\ \large m = 15

Question Type

Answer Box

Variables

Variable nameVariable value
question
In this inequality $\large m$ is a whole number. >$\dfrac{11}{\large m} < \dfrac{3}{4}$
What is the smallest possible value for $\large m$ to make this inequality true?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{11}{\large m}$ | < $\dfrac{3}{4}$ | | $3\large m$ | > 44 | | $\large m$ | > $\dfrac{44}{3}$ | | $\large m$ | > 14.66... |

$\therefore$ Smallest $\ \large m$ = {{{correctAnswer0}}}
correctAnswer0
15
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer015

Variant 4

DifficultyLevel

734

Question

In this inequality q\large q is a whole number.

75>9q\dfrac{7}{5} > \dfrac{9}{\large q}


What is the smallest possible value for q\large q to make this inequality true?

Worked Solution
75\dfrac{7}{5} > 9q\dfrac{9}{\large q}
7q7\large q > 45
q\large q > 457\dfrac{45}{7}
q\large q > 6.428...

∴\therefore Smallest  q\ \large q = 7

Question Type

Answer Box

Variables

Variable nameVariable value
question
In this inequality $\large q$ is a whole number. >$\dfrac{7}{5} > \dfrac{9}{\large q}$
What is the smallest possible value for $\large q$ to make this inequality true?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{7}{5}$ | > $\dfrac{9}{\large q}$ | | $7\large q$ | > 45 | | $\large q$ | > $\dfrac{45}{7}$ | | $\large q$ | > 6.428... |

$\therefore$ Smallest $\ \large q$ = {{{correctAnswer0}}}
correctAnswer0
7
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer07

Variant 5

DifficultyLevel

738

Question

In this inequality d\large d is a whole number.

1123>5d\dfrac{11}{23} > \dfrac{5}{\large d}


What is the smallest possible value for d\large d to make this inequality true?

Worked Solution
1123\dfrac{11}{23} > 5d\dfrac{5}{\large d}
11d11\large d > 115
d\large d > 11511\dfrac{115}{11}
d\large d > 10.45...

∴\therefore Smallest  d\ \large d = 11

Question Type

Answer Box

Variables

Variable nameVariable value
question
In this inequality $\large d$ is a whole number. >$\dfrac{11}{23} > \dfrac{5}{\large d}$
What is the smallest possible value for $\large d$ to make this inequality true?
workedSolution
| | | | -------------: | ---------- | | $\dfrac{11}{23}$ | > $\dfrac{5}{\large d}$ | | $11\large d$ | > 115 | | $\large d$ | > $\dfrac{115}{11}$ | | $\large d$ | > 10.45... |

$\therefore$ Smallest $\ \large d$ = {{{correctAnswer0}}}
correctAnswer0
11
prefix0
suffix0

Answers

Specify one or more 'ANSWER' block(s) as exampled below.
Note: correctAnswer is required, the rest are optional. ("correctAnswer" is what the student would need to type in to the box to get the answer correct.)

For example:
correctAnswer: 123.40

And optionally, specify the following, but only if you need something different to the defaults: 'width' defaults to 5 if not present, and valid values are 3 to 10; 'prefix' and 'suffix' default to nothing if not present.
prefix: $
suffix: mm$^2$
width: 5

correctAnswerNcorrectAnswerValueAnswer
correctAnswer011

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