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Browse High School Basic Algebra
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Solving simple linear equations.
Positive/negative integer rules.
Mixture problems.
Quadratic equations.
Absolute value.
Completing the square.
Direct and indirect variation.
Inequalities and negative numbers.
 Discriminants [10/22/1996]

Find the discriminant and determine the nature and the number of roots of
2x^2+x6 = 0 without solving the equation.
 Distance Between a Point and a Line [08/23/1998]

Find the distance between the origin and the line 3x + 4y = 5.
 Distance Between Telephone Poles [4/15/1995]

If you have 6 equally spaced telephone poles, and the distance between
the first and sixth telephone pole is 1260 feet, what is the distance
between the first and fourth telephone poles?
 Distribution and Absolute Values [09/22/1999]

Is it okay to distribute through an absolute value sign? For example, is
23x+1 = 6x+2?
 Distributive Property [10/29/1997]

I don't understand the Distributive Property at all.
 Distributive Property [10/13/2001]

We are learning the distributive property in school. Why do we have to
learn this, and how will we use it, and when?
 Distributive Property with Negatives [10/13/2004]

When using the distributive property with negative numbers, I don't
understand when, why, and how the operator changes (from addition to
subtraction, or the other way). Sometimes it changes, sometimes it
doesn't. Can you explain when to change it, and why?
 Distributive Property: (x+2)(x+4) [09/18/2001]

I'm confused about the distributive property. Example: (x+2)(x+4).
 Dividing Polynomials [03/06/1997]

The polynomial p(x) with integer coefficients satisfies (1) if p(x) is
divided by x^24x+3, the remainder is 65x68, and (2) if p(x) is divided
by x^2+6x7, the remainder is 5x+a. Find a.
 Dividing the Prize Money [05/24/2000]

Mrs. Shoe gave her prize winnings to her children in order... and all the
prize money was divided equally amongst her children. How many children
were there?
 Divisibility by 37 [11/08/1997]

Take a 3digit number and add to that its "rotation". Prove that the sum
can always be divided by 37.
 Division of Polynomials [8/10/1995]

Please send me some examples of polynomial divisions.
 Domain of a Function [9/13/1996]

What is the domain of f(x)= x/sqrt(x^24)?
 Domain/Range of a Function [01/22/1997]

How do you find the domain and range of the function f(x) = 2x^23x+1?
(Both with and without calculus.)
 Don't Multiply by Zero [01/23/2002]

Solve for y: 3y/y7  3/2 = 21/y7. I get 21/03/2 = 21/0.
 Double Quadratic Equation [7/5/1996]

Is there a simple solution to ax^2 + bx + cy^2 + dy + e = 0?
 Doubling Opposite Integers [04/19/1998]

On a number line, a certain integer is 24 units away from the double of
its opposite. What is the integer?
 The Egyptians' Method of False Position [01/16/2003]

How does the method of false position work?
 Electrical Relationships [12/10/1996]

The resistance in an electrical circuit is related to the diameter of the
wire and the length of the wire. How does resistance vary with diameter?
 An Ellipse Or A Circle?  Parametric Equations [12/05/1998]

Is this parametric equation elliptical or a circle?... And how do I
compute the slopes at points 0, pi/4, pi/2, 3pi/2,and 2pi?
 Empty Set Classification [2/20/1995]

We would like to know if you would classify an empty set as being finite,
infinite, or with another classification.
 Empty Sets [08/15/1997]

Can you help me understand empty sets?
 Enlarging the Penguin Pond [06/03/1999]

By how much should its length and width be increased to double the area
of the 12 meter x 8 meter penguin pond at the zoo?
 Equal Sum, Product, Quotient of Two Numbers [10/13/2002]

I need to know the sum, product, and quotient, all equal, of two
different numbers.
 Equation for an Arch [09/09/1997]

I am trying to draw an arch that will go in the ceiling of a building.
The arch will be at a maximum height of 28 inches...
 Equation for undefined slope [10/24/1999]

How do you write an equation for a vertical line with an undefined slope?
For example, a vertical line with an xintercept of 8.
 Equation of a Line in PointSlope, SlopeIntercept, General Form [8/2/1996]

What is the equation of the line that contains the point (4, 4) and is
perpendicular to the line defined by 2x5y+3 = 0?
 Equation of a Parabola [03/04/1997]

Determine the equation of a parabola given its vertex and either the
equation of the directrix or the coordinates of the focus.
 Equation Roots [01/22/2001]

How do you get the real, imaginary, rational, and irrational(roots) of
the equation?
 Equations for Lines [5/29/1996]

Write an equation of the line containing the point P(1,3)...
 Equation Solving Steps [04/28/1997]

Solve for x in the equation: 42(x2b) = ax+3.
 Equations [5/24/1996]

a) 7(4y+69)8(2y3) = 5(3y+7); b) (2x5)(3x+2) = (6x+1)(x7); c)
(3x2)(3x+2)+(x+4)(x5) = (5x1)(2x3)
 Equations That Make No Sense [01/15/2003]

Solve for x: x8/5 = x+2/6.
 Equations with Absolute Value [01/24/1999]

I know that if an equation has an absolute value, you need to have a
positive and a negative part when you solve it. How do you get both
answers?
 Equations with Two Variables [03/25/1998]

Identify and find solutions to systems of equations or inequalities by
graphing.
 Equilateral Triangles [6/22/1996]

Draw an equilateral triangle of side n units...
 Etymologies of Algebra, Geometry, Trigonometry [10/22/2001]

What are the origins and roots of the words geometry, algebra, and
trigonometry?
 Examination Puzzle [02/14/2003]

Three students take an examination in N subjects... How many subjects
were there, and how many points did each student get?
 Examples and Explanations of Basic Properties of Equality [07/31/2004]

Can you explain the substitution, symmetric, and transitive properties
of equality in simpler terms?
 Exchanging Seats in a Boat [06/08/2001]

Ten women are fishing in a long, narrow boat. One seat in the center of
the boat is empty. The five women in the front of the boat want to change
seats with the five women in the back of the boat...
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