







The area of a patio 
20190623 

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 
20180920 

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. 





An inequality 
20150419 

From mr.: Simplify the inequality √x>x and represent on a number line Answered by Penny Nom. 





An inequality 
20140327 

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 
20140125 

From LANELL: this is a problem to solve: 1/3 + 2/7 >=x/21  part of the answer is (oo)
not exactly that similarit 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 
20140117 

From Rosie: 4x/x2<3
four x divided by x2 is less than or equal to 3 Answered by Penny Nom. 





When would one flip the inequality sign? 
20140109 

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
THANKS! Answered by Penny Nom. 





Changing the sign of an inequality 
20120919 

From Bryauna: Why do you change the signs in inequalities?! Answered by Penny Nom. 





A cubic inequality 
20120325 

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. 





An inequality 
20101213 

From jimmy: 1.7b1.1 <2.3 Answered by Stephen La Rocque. 





Graphing a linear inequality 
20100526 

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 (x2) / (x+4) <7 
20100523 

From Rocco: Which values of x satisfy (x2) / (x+4) <7 Answered by Harley Weston. 





Frank makes picture frames 
20100220 

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 
20100201 

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. 





The triangle inequality 
20100111 

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. 





e^pi and pi^e 
20091022 

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(x4)>4+2x 
20090827 

From jorna: 2(x4)>4+2x Answered by Penny Nom. 





Things equal to the same thing 
20090729 

From nazrul: If p^2pa+q=0 and m^2ma+n=0 , can we write p^2pa+q= m^2ma+n? Please explain. Answered by Robert Dawson. 





Inequalities Proof 
20090724 

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. 





Properties of Inequality 
20090605 

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 
20090516 

From Nazrul: What is the solution of absolute value of (1/(x+1))<1? Please explain. Answered by Stephen La Rocque. 





An inequality with logs 
20090306 

From Indrajit: (x/10)^(logx  2)<100..........how to solve this one?? Answered by Stephen La Rocque. 





Solving an equality 
20090210 

From Deborah: 2(v+10)<18 Answered by Penny Nom. 





Solving an inequality 
20090102 

From jarred: 3x+8>2 Answered by Penny Nom. 





5x < 25+10 
20080425 

From Courtney: What is the answer to 5x<25+10 Answered by Stephen La Rocque. 





The isoperimetric inequality 
20080421 

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 
20080401 

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 
20080220 

From ed: solve the inequality
(x+3)^2 (2x)
___________ < 0
(x+4) (x^2  4)
Answered by Penny Nom. 





Multiplying an inequality by a negative number 
20071127 

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. 





Equality of sets 
20070723 

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. 





An inequality 
20070616 

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 
20070517 

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. 





3x > 12 
20070111 

From Jen: In the following inequality, would one flip the inequality symbol?
3x > 12 Answered by Stephen La Rocque. 





x + 2y < 6 
20070106 

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 
20061207 

From Carol: S(n) = 2^n > 10n+7 and n>=10 Answered by Stephen La Rocque. 





Linear inequalities 
20061201 

From Susan: how would I graph a linear inequality of y>3. Answered by Stephen La Rocque. 





2x > 6 and x  4 < 3 
20061127 

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. 





Inequalities 
20061003 

From Maleeha: a)Use algebra to find the set of values of 'x' for which x(x5)>36.
b)Using your answer to part a, find the set of values 'y' for which y^{2}(y^{2}5)>36 Answered by Penny Nom. 





Graphing a linear inequality 
20050826 

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? 
20050818 

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? 
20050529 

From Linda: Which number is greater 31^{11} or 17^{14} (without using
calculator). Answered by Chris Fisher and Paul Betts. 





Graphing an inequality 
20050502 

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 
20050331 

From Ambross: demostrate the following inequality:
2.Sqrt(K+1)2.Sqrt(k)<1/Sqrst(K)<2.Sqrt(K)2.Sqrt(k1)
Answered by Penny Nom. 





Graphing inequalities 
20050215 

From Melanie: Solve and Graph the following variable inequalities:
y<2x+4
y>2x+6
3x+4y<24
4x6y>24 Answered by Penny. 





An ineqlality with absolute values 
20040705 

From Uneeza: abs(x^{2}  4x) > 3 Answered by Claude Tardif. 





Solving inequalities 
20040503 

From Joe: Let x be a real number find and graph the solution to the following sentances:
2x10+9
4X+2<15
5X+3>(x1) Answered by Peny Nom. 





Inequalities 
20040108 

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 
20031125 

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 
20031107 

From A student: In the ratio 3:8=17__, can__be a whole number? Answered by Penny Nom. 





Cathy's Clothing 
20030715 

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 
20030408 

From Jessica: Solve for x. Write in interval notation.
[(x^{2})9]/[x5] >= 0 Answered by Penny Nom. 





y < 2x + 1 
20030301 

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 
20021013 

From Veronica: Solve the following inequality: 5(xsqured4)/(xto the 5th(2x5)to the 3rd) < or equal 0 Solve the following equations for all roots square root of x+2=1+square root of 2x+3 what's ZERO FACTOR PROPERTY??? The hypotenuse of an isosceles right triangle is 7cm. long. Determine the lenghts of the other sides. Answered by Leeanne Boehm. 





When does an inequality represent the area above the line? 
20020825 

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 
20020725 

From A student:
1)5 <= 3X+1 < 1 2)4X2 < 6 OR X+2 > 9 Answered by Penny Nom. 





Inequalities 
20011113 

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? 
20011026 

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. 





The triangle inequality 
20010927 

From A student:
__ __ __
Prove that AX + XB = AB for any X on AB.
Answered by Chris fisher. 





A linear inequality 
20010917 

From Eric: How can I solve x + y + x  y< =6? Answered by Penny Nom. 





An inequality involving triangles 
20010612 

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 
20010212 

From A student: If 3 Answered by Leeanne Boehm. 





Which fraction is greater? 
20010201 

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 
20010116 

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. 





Inequalities 
20000902 

From Jennifer: I would like some help with equations and inequalities. My first inequality is 3p6>21 and 3q+11+8q>99. Answered by Paul Betts. 





Graphing an inequality 
20000802 

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? 
20000405 

From An elementary student: What is the mathematical reason equivalent fractions are equal? Answered by Penny Nom. 





62x<4 
19991020 

From Tchilco: Solve 62x<4 Answered by Harley Weston. 





Standard Deviation 
19990711 

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. 
19990306 

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 
19970324 

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? 
19960517 

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. 

