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Solving an inequality 2020-10-18
From nunya:
3(4 + 2n) > 2n - 16
Answered by Penny Nom.
A system of inequalities 2020-02-01
From Isaac:
Austin has x nickels and y dimes, having a maximum of 15 coins worth a minimum of $1 combined. No more than 4 of the coins are nickels and no less than 11 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
Answered by Penny Nom.
The area of a patio 2019-06-23
From Miguel:
Stephanie has 60 feet of metal fencing material to only fence 3 sides of a rectangular patio. A tall metal wall serves as the fourth side of the rectangle. write a function for the area the garden (A) in terms of width in feet (x) What measures of the width would give an area of at least 150 feet?
Answered by Penny Nom.
An inequality with no solution 2018-09-20
From Alena:
I'm trying to help with a homework problem. Can you please help me?

2kx - 3k < 2x + 4 +3kx

We are solving for "k" with no solution.

Answered by Penny Nom.
A pair of linear inequalities 2017-08-08
From Hempstone:
Solve the inequalities 3x-5<2x+5>4x+9
Answered by Penny Nom.
A quadratic equation with equal roots 2016-01-23
From abdiwahid:
X^2+2ax+4x+9a=0 is quadratic equation which has equal roots. Find the possible value of a?
Answered by Penny Nom.
An inequality 2015-04-19
From mr.:
Simplify the inequality √x>x and represent on a number line
Answered by Penny Nom.
A region described by inequalities in cylindrical coordinates 2015-02-21
From Rahul:
I am not able to visualize a solid given by inequalities as under (in cylindrical coordinate system) 0= I know that (can visualize) first 2 inequalities say it is a cylinder of infinite length. It seems that third inequality poses the restriction to the height as well as it makes us to remove a cone.
But I just can not understand it clearly.
Thanks in advance!

Answered by Penny Nom.
An equilateral triangle with vertices in 3 parallel planes 2014-05-31
From prajay:
How to construct an Equilateral Triangle whose vertices lie on three parallel lines, if the distances of two lines are 'a' and 'b' units from the middle line.What is the length of the side of the Equilateral Triangle ?
Answered by Chris Fisher.
An inequality 2014-03-27
From James:
a step on a stairway is at least 8 inches high. write and solve an inequality to represent the maximum number of steps between floors that are 10 feet apart
Answered by Penny Nom.
An inequality 2014-01-25
this is a problem to solve: 1/3 + 2/7 >=x/21 -- part of the answer is (-oo) not exactly that similar--it is on a calculator as a symbol- sure you know what it is I am talking about- the x will be a number
Answered by Penny Nom.
An inequality 2014-01-17
From Rosie:

four x divided by x-2 is less than or equal to 3

Answered by Penny Nom.
When would one flip the inequality sign? 2014-01-09
From Natasha:
Would one flip the inequality symbol in this equation: (explain why) (-9a)/(-9) > 81
And please explain in what circumstances one would flip the inequality sign

Answered by Penny Nom.
Equal ordinate and abscissa 2013-08-15
From sonit:
the slope of tangent to the curve y=(4-x^2)^1/2 at the point, where the ordinate and abscissa are equal, is
Answered by Penny Nom.
Solve 2x^4+x^3-37x>26x^2+12 using a graphical approach. 2012-12-29
From Tehmas:
Solve 2x^4+x^3-37x>26x^2+12 using a graphical approach.
I don't know how to find the x-intercepts or y-intercepts in this form.

Answered by Penny Nom.
-5<2x+1<-1 2012-11-11
From Rahul:
How does -5<2x+1<-1 changes to 1<|2x+1|<5. What is the rule? Can we apply absolute value function throughout the first inequality i.e. can we say |-5|<|2x+1|<|-1|. But then it becomes 5<|2x+1|<1 which is impossible because 5 is not less than 1.
Answered by Penny Nom.
A proof by contraposition 2012-10-19
From Rahul:
I am not able to understand the following,
To prove that if for all e>0, |x|0, then |x|>=e. I understand the approach very well but I do not understand why if |x|=e then |x|>=e. If it is so then why not |x|= Thanks in advance!'

Answered by Penny Nom.
Changing the sign of an inequality 2012-09-19
From Bryauna:
Why do you change the signs in inequalities?!
Answered by Penny Nom.
A cubic inequality 2012-03-25
From Victoria:
The flight path of a bumblebee above the ground can be modelled by the function f(x)= 2x^3- 17x^2+ 11x + 130. Where x is the time in seconds and f(x) represents the height in inches above the ground. The entrance to the bee's hive is located 100 inches above the ground. Determine when the bumblebee's height is greater than 100 inches. The bee's height was monitored from 0 to 25 seconds inclusive. (over the domain 0
Answered by Penny Nom.
Linear inequalities 2011-03-25
From Alice:
OK. I'm in algebra 1 and the linear inequality is
I don't completely know how to graph y>2 and I'm getting really frustrated
Please help me in any way possible!
Thank You!

Answered by Penny Nom.
An inequality 2010-12-13
From jimmy:
1.7b-1.1 <2.3
Answered by Stephen La Rocque.
Linear inequalities with absolute values 2010-12-01
From ryan:
Good day!
We we're given this assignment in algebra concerning linear inequalities with absolute value. In this number I'm confused how to isolate the absolute value, considering there is a variable in the absolute value and there is a variable in the outside.

2+5 |4-3t|+t ≤ -3-4t

Answered by Penny Nom.
4 > -3m-7 >= 2 2010-06-05
From pamela:
The question is

Answered by Penny Nom.
Graphing a linear inequality 2010-05-26
From Valeie:
When graphing a linear inequality, how do you know if the inequality represents the area above the line.
Answered by Penny Nom.
Which values of x satisfy (x-2) / (x+4) <7 2010-05-23
From Rocco:
Which values of x satisfy (x-2) / (x+4) <7
Answered by Harley Weston.
Frank makes picture frames 2010-02-20
From Carol:
Frank makes picture frames his revenue from sales is R=$13.60x for frames sold. The cost making frames is C=$5.80x+$120 for frames made. What is the minum number of frames Frank must make and sell in order for his revenue to be greater than his costs.
Answered by Penny Nom and Melanie Tyrer.
1/a + 1/b + 1/c < 1 2010-02-01
From Mrityun:
suppose a,b and c are natural numbers such that 1/a + 1/b + 1/c < 1. Prove that

1/a + 1/b + 1/c < = 41/42.

Answered by Penny Nom and Claude Tardif.
Growth rates 2010-01-26
From Bhavya:
Dear Sir/Ma'am,

I read in the text book that the growth rates of these 3 functions are as below- n2/3 < n/lg n < n0.99

I tried the substitution method to check the correctness of this. But it gets really tough as n increase.

Is there any simpler way to understand the correctness of these growth rates?

Thanks and Regards,

Answered by Robert Dawson.
The triangle inequality 2010-01-11
From Nazrul:
If A and B are any two vectors, then how can I prove that magnitude of (A+B)<=magnitude of A+magnitude of B. Please show me the process in details. Thank you.
Answered by Robert Dawson.
Cutting a square into four shapes 2010-01-05
From Tracy:
A square with a side of 4 ft needs to be cut into four shapes with the same area. can you find six different was to cut the square?
Answered by Robert Dawson.
e^pi and pi^e 2009-10-22
From Natalie:
Question from natalie, a student:

Without using your calculator, prove which is bigger: e^pi or pi^e

we talked about ad absurdum in class, so I'm assuming that is how I approach this question, but since neither of them have a variable( like the examples we actually solved in class), I'm not quite sure how to solve it....

Answered by Harley Weston.
2(x-4)>-4+2x 2009-08-27
From jorna:
Answered by Penny Nom.
Things equal to the same thing 2009-07-29
From nazrul:
If p^2-pa+q=0 and m^2-ma+n=0 , can we write p^2-pa+q= m^2-ma+n? Please explain.
Answered by Robert Dawson.
Inequalities Proof 2009-07-24
From ABOU:
good morning.......a b c are real positive no zero......proof that sq root(2a/(a+b))+sq root(2b/(b+c))+sq root(2c/(c+a))inferior or equal 3 thank you
Answered by Janice Cotcher.
Inequalities 2009-07-22
From Sindhu:
prove that 4^79 < ( (2^100) + (3^100) )< 4^80 ?
Answered by Robert Dawson.
Properties of Inequality 2009-06-05
From Nazrul:
We know that if a>b then (1/a)<(1/b) But why 5> -2 implies (1/5)>(1/-2) . Thank you in advance for your help.
Answered by Robert J. Dawson.
|1/(x+1)| <1 2009-05-16
From Nazrul:
What is the solution of absolute value of (1/(x+1))<1? Please explain.
Answered by Stephen La Rocque.
Solve -1<5-2x<10 for x 2009-05-12
From Helen:
solve the following inequality for x
-1<5-2x<10 Te less then sign by the one, should be less then or equal to.

Answered by Stephen La Rocque and Penny Nom.
Four identical lots 2009-03-30
From Marina:
I really want to know the answer to this problem for my 6th grade son. I've already sent this question with the drawing but I couldn't send it correctly. I hope this one will pass through. Q: Divide evenly and identical the figure representing a lot, into four for the 4 siblings. I've sent a figure drawing as attachment. I will describe this in case it will not reach you: its a square divide into 4 triangle and 1 triangle is taken out living a letter M figure and this letter M figure is the one that will be divided.into 4 even and identical parts.


Answered by Claude Tardif.
An inequality with logs 2009-03-06
From Indrajit:
(x/10)^(logx - 2)<100..........how to solve this one??
Answered by Stephen La Rocque.
Solving an equality 2009-02-10
From Deborah:
Answered by Penny Nom.
Solving an inequality 2009-01-02
From jarred:
Answered by Penny Nom.
What are the equivalent to 0.68? 2008-10-28
From clay:
what are the equivalent to 0.68 ?
Answered by Penny Nom.
Two inequalities 2008-10-08
From s:
3y > 4x

Answered by Stephen La Rocque.
How do you solve for x when (x^4)-x is greater than or equal to 0? 2008-08-14
From Katie:
How do you solve for x when (x^4)-x is greater than or equal to 0?
Answered by Penny Nom.
-5x < 25+10 2008-04-25
From Courtney:
What is the answer to -5x<25+10
Answered by Stephen La Rocque.
How is the square root of 3/4 is greater than 3/4? 2008-04-22
From Serena:
How is the square root of 3/4 is greater than 3/4?
Answered by Penny Nom.
The isoperimetric inequality 2008-04-21
From Dutch:
I'm searching for the proof that the sphere has the smallest volume of any figure and maximizes the volume of any figure.
Answered by Chris Fisher.
Two consecutive odd numbers 2008-04-01
From prinsilla:
of all pairs of consecutive odd integers whose sum is greater than 75. find the pair whose sum is least?
Answered by Stephen La Rocque.
A fractional inequality 2008-02-20
From ed:
solve the inequality
(x+3)^2 (2-x)
___________ < 0
(x+4) (x^2 - 4)

Answered by Penny Nom.
Multiplying an inequality by a negative number 2007-11-27
From Lisa:
Why is it that you have to switch the sign of the inequality when you divide or multiply by an negative number to solve for a variable?
Answered by Penny Nom and Walter Whiteley.
Variable expressions - part 2 2007-09-04
From lisa:
how do I write a variable expression for word phrase example x less than = 2 or 2 less than p 4 fewer than job please help
Answered by Penny Nom.
Three points on the circumference of a circle 2007-07-30
From Bharathi:
given a circle with radius r and a point x,y on its circumference,output two other points x1,y1 and x2,y2 on the circle so thar all 3 points form a equilateral triangle.
Answered by Stephen La Rocque.
Equality of sets 2007-07-23
From Mac:
Hi, I learnt set theory recently. My teacher and few of the weblink actually give different definition for basic set. Can you please solve this ?

My teacher says, {1,2,3} and {1,1,2,3} is also set.
But in this link http://library.thinkquest.org/C0126820/setsubset.html it says,
"A set has no duplicate elements. An element is either a member of a set or not. It cannot be in the set twice."
and "{1, 2, 3} is the same as the set {1, 3, 2, 3, 1}"

My question is,
1. Whether duplicates allowed in the set or not ?
2. Even if the duplicates are allowed, {1,2,3} and {1,1,2,2,3,3} are same or not ?

Answered by Penny Nom and Harley Weston.
Splitting the profits unequally 2007-06-27
From Maci:
We recently hosted a fundraiser. Not everyone will receive a whole share of the profits because they did not participate the entire time. Several will receive only 1/2 or 1/3 share. How do I divide the profits?
Answered by Stephen La Rocque.
Simultaneous inequalities 2007-06-18
From Freddy:
Watson Electric has production facilities in Valley Mills, Marlin,and Hillsboro. Each one produces radios,stereos,and TV sets. There production capacities are

Valley Mills: 10 radios, 12 stereos, and 6 TV sets per hour Marlin: 7 radios, 10 stereos, and 8 TV sets per hour Hillsboro: 5 Radios, 4 Stereos, amid 13 TV sets per hour


How many hours should each plant be scheduled to fill an order of 1095 radios, 1230 stereos, and 1490 TV sets?

Answered by Stephen La Rocque.
An inequality 2007-06-16
From jerry:
Two real numbers a and b satisfy the equation ab=1.
i) Prove that a^6 + 4b^6 >4
ii) Find out whether the inequality a^6 + 4b^6 >4 holds for all a and b such that ab = 1

Answered by Stephen La Rocque.
Altitudes of scalene triangles 2007-05-17
From Chris:
Two of the altitudes of a scalene triangle ABC have length 4 and 12. If the length of the third altitude is also an integer, what is the biggest that it can be?
Answered by J. Chris Fisher.
A linear system 2007-03-23
From Adam:
Solve the system by graphing:

Answered by Stephen La Rocque and Penny Nom.
3x > -12 2007-01-11
From Jen:
In the following inequality, would one flip the inequality symbol?

3x > -12

Answered by Stephen La Rocque.
x + 2y < 6 2007-01-06
From Mike:
I understand solving by graphing, but i am having trouble with the graphing of in equalities. i solved : x + 2y<6
Answered by Penny Nom.
The proof of inequality by mathematical induction 2006-12-07
From Carol:
S(n) = 2^n > 10n+7 and n>=10
Answered by Stephen La Rocque.
Linear inequalities 2006-12-01
From Susan:
how would I graph a linear inequality of y>3.
Answered by Stephen La Rocque.
2x > -6 and x - 4 < 3 2006-11-27
From Alyssa:
2x > -6 and x - 4 < 3 , i need to know how to solve it and how to graph it.
Answered by Stephen La Rocque.
"Less than" and "less than or equal to". 2006-11-15
From Ross:

7 ≤ 10 and 7 ≤ 7 are both true statements.

How can 7 be equal to 10, and 7 be less than 7? The book doesn't explain WHY!

Answered by Penny Nom.
Inequalities 2006-10-03
From Maleeha:
a)Use algebra to find the set of values of 'x' for which x(x-5)>36.
b)Using your answer to part a, find the set of values 'y' for which y2(y2-5)>36

Answered by Penny Nom.
Can one divide a circle into 4.5 parts 2006-03-30
From Chris:
If it is possible, can one divide a circle into say, 4.5 parts (with 4 equal parts and a half part)?
Or for that matter, for any integer, n, into n/2 parts as above?]

Answered by Walter Whiteley.
Open dots and closed dots 2005-09-29
From Cynthia:
When graphing the solutions of an inequality, what is the difference between an open dot and a closed dot?
Answered by Penny.
Graphing a linear inequality 2005-08-26
From Gina:
When graphing a linear inequality, how do you know if the inequality represents the area above the line?
Answered by Penny Nom.
Which number is greater? 2005-08-18
From Dante:
Which number is greater: 888....88 X 333...33 or 444.......44 x 666........67 (each of the numbers has 1989 digits)?
Answered by Claude Tardif.
Which is larger, 31^11 or 17^14? 2005-05-29
From Linda:
Which number is greater 3111 or 1714 (without using calculator).
Answered by Chris Fisher and Paul Betts.
50^99 and 99! 2005-05-23
From Romel:
Which number is greater, 5099 or 99!
Answered by Claude Tardif.
Graphing an inequality 2005-05-02
From Janice:
I need to know how to graph inequalities. I need to know just abot everything. From graphing an equation to shading.
Answered by Leeanne Boehm.
An inequality 2005-03-31
From Ambross:
demostrate the following inequality:

Answered by Penny Nom.
Graphing inequalities 2005-02-15
From Melanie:
Solve and Graph the following variable inequalities:





Answered by Penny.
Square roots and inequalities 2004-10-25
From Waheed:
Q1. What is the simplest way of finding a square root of any number using just a pen and paper? (I am asking this question because I browsed a few sites a didn't find any method that is simpler than the one I use. so I am just curious.)

Q2. Is it possible that you take an equation and turn it into an inequality by performing same mathematical operations on both sides?

Answered by Claude Tardif and Penny Nom.
Driving me crazy 2004-09-18
From Jerry:
This is driving me crazy!!! Someone told me of a number that can be divided EQUALLY by each of the following individual numbers: 1,2,3,4,5,6,7,8,9. what is that number?
Answered by Penny.
An ineqlality with absolute values 2004-07-05
From Uneeza:
abs(x2 - 4x) > 3
Answered by Claude Tardif.
Solving inequalities 2004-05-03
From Joe:
Let x be a real number find and graph the solution to the following sentances:

2x-10+9 4X+2<15 5X+3>(x-1)

Answered by Peny Nom.
Inequalities 2004-01-08
From Michael:
How do you use inequalities in your job and in your everyday life?
Answered by Penny Nom.
An inequality whose solution is all points 2003-11-25
From Katie:

Hi my name is Katie and I am in the 9th grade and I would like help on this question. Is it possible to have a system of inequalities whose solution is all points?

1.I need to know why (explanation)

2.how to do it(example)

Answered by Penny Nom.
Equal ratios 2003-11-07
From A student:
In the ratio 3:8=17__, can__be a whole number?
Answered by Penny Nom.
Cathy's Clothing 2003-07-15
From Cathy:
I am supposed to write a practical and useful word problem that would use the following algebriac inequality to solve it: 12x + 25 > 15x + 10. State the quanity that represents x and solve the inequality.
Answered by Penny Nom.
A fractional inequality 2003-04-08
From Jessica:
Solve for x. Write in interval notation.

[(x2)-9]/[x-5] >= 0

Answered by Penny Nom.
Divide a circle in 8 equal pieces 2003-04-04
From Naomi:
I have to divide a circle in 8 equal pieces but can only cut 3 times
can you please help me

Answered by Penny Nom.
y < 2x + 1 2003-03-01
From Erika:
how can I solve and graph y<2x+1 and which side in the graph should i shade after i finish solving my inequality?
Answered by Penny Nom.
Three algebra problems 2002-10-13
From Veronica:
Solve the following inequality:

5(xsqured-4)/(xto the 5th(2x-5)to the 3rd) < or equal 0

Solve the following equations for all roots

square root of x+2=-1+square root of 2x+3


The hypotenuse of an isosceles right triangle is 7cm. long. Determine the lenghts of the other sides.

Answered by Leeanne Boehm.
< and > 2002-08-30
From Kelsey:
What is the origin of the greater (>) than and less (<) than signs?
Answered by Harley Weston.
When does an inequality represent the area above the line? 2002-08-25
From Tamara:
How do you determine that an inequality represents the area above the line and when do you include the line in the solution?
Answered by Penny Nom.
Some inequalities 2002-07-25
From A student:

1)-5 <= -3X+1 < 1

2)4X-2 < 6 OR X+2 > 9

Answered by Penny Nom.
Inequalities 2001-11-13
From Pat:
When writing the solution to an inequality, why is the solution written in set notation? {x/ }
Answered by Penny Nom.
Why do you flip the inequality sign? 2001-10-26
From Sean:
I have a question about an inequality problem. Here it is: Solve and graph 5 - 3x => 17. (=> is greater than or equal). Please tell me why you flip the inequality sign when divinding by a negative number.
Answered by Penny Nom.
Dividing a circle 2001-10-17
From Ahmeen:
I am having a hard time figuring out how a circle can be divided into 11 equal parts with only 4 cut allowed? My teacher gave this to us and I still can't cut my pie into eleven equal parts with only four cuts.
Answered by Walter Whiteley.
The triangle inequality 2001-09-27
From A student:
           __   __   __ 
Prove that AX + XB = AB for any X on AB.  

Answered by Chris fisher.
A linear inequality 2001-09-17
From Eric:
How can I solve |x + y| + |x - y|< =6?
Answered by Penny Nom.
An inequality involving triangles 2001-06-12
From Sandra:
The triangle inequality guarantees that the sum of the lengths of two sides of a triangle is greater than the length of the third. As a consequence, if x and y are legs of a right triangle, with x less than or equal to y, and z the hypotenuse, then x + y is greater than z, so x is greater than z - y. Under what circumstances will x is greater than 2(z - y) be true?
Answered by Chris Fisher and Penny Nom.
Two inequalities 2001-02-12
From A student:
If 3
Answered by Leeanne Boehm.
Which fraction is greater? 2001-02-01
From Carol:
Hello My name is Carol I am a student teacher! I am asked to aproach these students on their problems. I am unsure of how to explain to them that these are wrong. Can you help? Thanks.

Iris claims that if we have two positive rational numbers, the one with the greatest numerator is the greatest.

Shirly claim that if we have two positive rational numbers, the one with the greatest denominator is the least. Thanks!

Answered by Claude Tardif.
A problem with distance 2001-01-16
From A student:
For what values of a is the distance between P(a, 3) and Q(5, 2a) greater than the square root of 26.
Answered by Penny Nom.
< and > Which one is which? 2000-12-06
From Alice:
This grandmother forgot and wants to know the correct for greater and the one for lesser.....

the two are < and > Which one is which?

Answered by Penny Nom.
Larger and smaller 2000-10-10
From Nicole:
which one of these arrows < , > points to the greater number? which arrows points to the smaller number.
Answered by Penny Nom.
Inequalities 2000-09-02
From Jennifer:
I would like some help with equations and inequalities. My first inequality is 3p-6>21 and 3q+11+8q>99.
Answered by Paul Betts.
Graphing an inequality 2000-08-02
From Lori:
How do I find x and y and graph this problem

3x + y < 5

Answered by Penny Nom.
Why are equivalent fractions equal? 2000-04-05
From An elementary student:
What is the mathematical reason equivalent fractions are equal?
Answered by Penny Nom.
Inequalities and absolute values 1999-12-07
From Austin Cline:
Solve for x: The absolute value of x-1 is less than or equal to the absolute value of x-2
Answered by Harley Weston.
Cutting a board into 8 equal pieces 1999-10-21
From Brittany:
Jamie wanted a board cut into 8 equal pieces. The Lucas Lumber Co. charges 60 cents for cutting a board into 4 equal pieces. How much will it charge for cutting Jamie's board?
Answered by Claude Tardif.
|6-2x|<4 1999-10-20
From Tchilco:
Solve |6-2x|<4
Answered by Harley Weston.
Notation 1999-09-03
From Judy Gray:
My name is Judy Gray. I guess the level on this would be about middle school, and I am an other!! I've been out of school for alot of years. I have a couple of questions, I guess.
  1. What does an equal (=) with a slash through it mean? I put intersects, but I think I'm wrong.

  2. What is the symbol of a small n? Only the symbol is wider. Example: If A = {1.2} B = {2,3} then what is A (n) B? Can you make sense out of that?

  3. What is the equation of the y-axis?

Answered by Penny Nom.
Standard Deviation 1999-07-11
From Anthony Fama:
I have seen several answers to this question: If one standard deviation represents 68% of the population, what does two, three, four and five sigma [std deviation] represent? As stated, I have seen several different answers and thus, the impetus for my question.
Answered by Harley Weston.
Reversing the direction of an inequality. 1999-03-06
From Mallory White:
If the Problem was -4a plus -5 is less than or equal to 14, why would you change the sign to greater than or equal to?
Answered by Jack LeSage and Harley Weston.
Graphing Inequalities of Conic Sections 1997-03-24
From James Sheldon:
I'm trying to graph Systems of Conic Sections with inequalities, but I'm running into problems on which area to shade:
x^2+y^2 is greater than or equal to 16
xy > 4

So I graph these two equations, and then my teacher said to substitute a point into it but I'm still not sure how to do it...
Answered by Penny Nom.

How do you graph these inequalities? 1996-05-17
From Robert:
How do you graph the inequalities 5+gg, and g+h>6 on one coordinate plane?
Answered by Harley Weston and Maxine Stinka.



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