







A system of inequalities 
20200201 

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 
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. 





A pair of linear inequalities 
20170808 

From Hempstone: Solve the inequalities 3x5<2x+5>4x+9 Answered by Penny Nom. 





An inequality 
20150419 

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 
20150221 

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!
Regards,
Rahul 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 
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. 





Solve 2x^4+x^337x>26x^2+12 using a graphical approach. 
20121229 

From Tehmas: Solve 2x^4+x^337x>26x^2+12 using a graphical approach.
I don't know how to find the xintercepts or yintercepts in this form. Answered by Penny Nom. 





5<2x+1<1 
20121111 

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 
20121019 

From Rahul: I am not able to understand the following,
To prove that if for all e>0, x0, 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!'
Rahul. 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. 





Linear inequalities 
20110325 

From Alice: OK. I'm in algebra 1 and the linear inequality is
y<2x1
y>2
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 
20101213 

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





Linear inequalities with absolute values 
20101201 

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 43t+t ≤ 34t Answered by Penny Nom. 





4 > 3m7 >= 2 
20100605 

From pamela: The question is
4>3m7>=2 Answered by Penny Nom. 





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. 





Growth rates 
20100126 

From Bhavya: Dear Sir/Ma'am,
I read in the text book that the growth rates of these 3 functions are as below
n^{2/3} < n/lg n < n^{0.99}
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,
Bhavya Answered by Robert Dawson. 





2(x4)>4+2x 
20090827 

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





Inequalities 
20090722 

From Sindhu: prove that
4^79 < ( (2^100) + (3^100) )< 4^80 ? Answered by Robert Dawson. 





Solve 1<52x<10 for x 
20090512 

From Helen: solve the following inequality for x
1<52x<10 Te less then sign by the one, should be less then or equal to. Answered by Stephen La Rocque and Penny Nom. 





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. 





Two inequalities 
20081008 

From s: 3y > 4x
2x3y>6 Answered by Stephen La Rocque. 





How do you solve for x when (x^4)x is greater than or equal to 0? 
20080814 

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 
20080425 

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? 
20080422 

From Serena: How is the square root of 3/4 is greater than 3/4? Answered by Penny Nom. 





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. 





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. 





Variable expressions  part 2 
20070904 

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. 





Simultaneous inequalities 
20070618 

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
QUESTION
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 
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. 





A linear system 
20070323 

From Adam: Solve the system by graphing: 4y>6x
3x+2y<6 Answered by Stephen La Rocque and Penny Nom. 





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. 





Open dots and closed dots 
20050929 

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 
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. 





50^99 and 99! 
20050523 

From Romel: Which number is greater, 50^{99} or 99! Answered by Claude Tardif. 





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. 





Square roots and inequalities 
20041025 

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. 





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. 





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. 





A linear inequality 
20010917 

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





< and > Which one is which? 
20001206 

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 
20001010 

From Nicole: which one of these arrows < , > points to the greater number? which arrows points to the smaller number. 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. 





Inequalities and absolute values 
19991207 

From Austin Cline: Solve for x: The absolute value of x1 is less than or equal to the absolute value of x2 Answered by Harley Weston. 





62x<4 
19991020 

From Tchilco: Solve 62x<4 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. 

