<< Chapter < Page Chapter >> Page >

Section exercises

Verbal

When solving an inequality, explain what happened from Step 1 to Step 2:

Step 1 2 x > 6 Step 2 x < 3

When we divide both sides by a negative it changes the sign of both sides so the sense of the inequality sign changes.

Got questions? Get instant answers now!

When solving an inequality, we arrive at:

x + 2 < x + 3 2 < 3

Explain what our solution set is.

Got questions? Get instant answers now!

When writing our solution in interval notation, how do we represent all the real numbers?

( , )

Got questions? Get instant answers now!

When solving an inequality, we arrive at:

x + 2 > x + 3 2 > 3

Explain what our solution set is.

Got questions? Get instant answers now!

Describe how to graph y = | x 3 |

We start by finding the x -intercept, or where the function = 0. Once we have that point, which is ( 3 , 0 ) , we graph to the right the straight line graph y = x −3 , and then when we draw it to the left we plot positive y values, taking the absolute value of them.

Got questions? Get instant answers now!

Algebraic

For the following exercises, solve the inequality. Write your final answer in interval notation.

3 x + 2 7 x 1

( , 3 4 ]

Got questions? Get instant answers now!

4 ( x + 3 ) 2 x 1

[ 13 2 , )

Got questions? Get instant answers now!

1 2 x 5 4 + 2 5 x

Got questions? Get instant answers now!

−5 ( x 1 ) + 3 > 3 x 4 4 x

( , 3 )

Got questions? Get instant answers now!

−3 ( 2 x + 1 ) > −2 ( x + 4 )

Got questions? Get instant answers now!

x + 3 8 x + 5 5 3 10

( , 37 3 ]

Got questions? Get instant answers now!

x 1 3 + x + 2 5 3 5

Got questions? Get instant answers now!

For the following exercises, solve the inequality involving absolute value. Write your final answer in interval notation.

| x + 9 | −6

All real numbers ( , )

Got questions? Get instant answers now!

| 3 x 1 | > 11

( , 10 3 ) ( 4 , )

Got questions? Get instant answers now!

| x 2 | + 4 10

( , −4 ] [ 8 , + )

Got questions? Get instant answers now!

| x 7 | < −4

No solution

Got questions? Get instant answers now!

| x 3 4 | < 2

( −5 , 11 )

Got questions? Get instant answers now!

For the following exercises, describe all the x -values within or including a distance of the given values.

Distance of 5 units from the number 7

Got questions? Get instant answers now!

Distance of 3 units from the number 9

[ 6 , 12 ]

Got questions? Get instant answers now!

Distance of10 units from the number 4

Got questions? Get instant answers now!

Distance of 11 units from the number 1

[ −10 , 12 ]

Got questions? Get instant answers now!

For the following exercises, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.

3 x + 1 > 2 x 5 > x 7

x > 6  and  x > 2 Take the intersection of two sets . x > 2 , ( 2 , + )

Got questions? Get instant answers now!

2 x 5 < −11     or     5 x + 1 6

x < 3 or x 1 Take the union of the two sets . ( , 3 ) [ 1 , )

Got questions? Get instant answers now!

Graphical

For the following exercises, graph the function. Observe the points of intersection and shade the x -axis representing the solution set to the inequality. Show your graph and write your final answer in interval notation.

| x 1 | > 2

( , −1 ) ( 3 , )


A coordinate plane where the x and y axes both range from -10 to 10.  The function |x  1| is graphed and labeled along with the line y = 2.  Along the x-axis there is an open circle at the point -1 with an arrow extending leftward from it.  Also along the x-axis is an open circle at the point 3 with an arrow extending rightward from it.

Got questions? Get instant answers now!

| x + 7 | 4

[ −11 , −3 ]


A coordinate plane with the x-axis ranging from -14 to 10 and the y-axis ranging from -1 to 10.  The function y = |x + 7| and the line y = 4 are graphed.  On the x-axis theres a dot on the points -11 and -3 with a line connecting them.

Got questions? Get instant answers now!

| x 2 | < 0

It is never less than zero. No solution.


A coordinate plane with the x and y axes ranging from -10 to 10.  The function y = |x -2| and the line y = 0 are graphed.

Got questions? Get instant answers now!

For the following exercises, graph both straight lines (left-hand side being y1 and right-hand side being y2) on the same axes. Find the point of intersection and solve the inequality by observing where it is true comparing the y -values of the lines.

x 2 > 2 x + 1

Where the blue line is above the orange line; point of intersection is x = 3.

( , −3 )


A coordinate plane with the x and y axes ranging from -10 to 10.  The lines y = x - 2 and y = 2x + 1 are graphed on the same axes.

Got questions? Get instant answers now!

1 2 x + 1 > 1 2 x 5

Where the blue line is above the orange line; always. All real numbers.

( , )


A coordinate plane with the x and y axes ranging from -10 to 10.  The lines y = x/2 +1 and y = x/2  5 are both graphed on the same axes.

Got questions? Get instant answers now!

Numeric

For the following exercises, write the set in interval notation.

{ x | −1 < x < 3 }

( −1 , 3 )

Got questions? Get instant answers now!

{ x | x < 4 }

( , 4 )

Got questions? Get instant answers now!

{ x | x  is all real numbers }

Got questions? Get instant answers now!

For the following exercises, write the interval in set-builder notation.

( , 6 )

{ x | x < 6 }

Got questions? Get instant answers now!

[ −3 , 5 )

{ x | −3 x < 5 }

Got questions? Get instant answers now!

[ −4 , 1 ] [ 9 , )

Got questions? Get instant answers now!

For the following exercises, write the set of numbers represented on the number line in interval notation.

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 4

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask