See also the
Dr. Math FAQ:
order of operations
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.
Completing the square.
Direct and indirect variation.
Inequalities and negative numbers.
- Compound Inequalities [09/10/1997]
Can you write compound inequalities that use "or" the same way you write
compound inequalities that use "and"?
- Compound Inequality [9/15/1996]
5x-1 > 4 and 6x+3 < 4x-1
- Concept of Factoring [03/22/1997]
Could you explain the concept of factoring and give examples of its
- Consecutive Integers [11/7/1995]
Finding consecutive integers.
- Consecutive Integers, Divisible by the Sums of Their Digits [05/20/2002]
Find the first three consecutive integers greater than 10, each of
which is divisible by the sum of its digits.
- Constructing Polynomials [01/20/1999]
I need to find polynomials given certain properties. For example, find a
polynomial P(x) that is of degree 4, where P(x) = P(-x), ...
- A Container Holds 5/8 Gallon... [11/05/1997]
If the container is 4/5 full and then 25 percent of the liquid is lost
due to evaporation, how much liquid is left in the container?
- Converting Seconds to MPH [07/11/2000]
I'm looking for a chart that converts the number of seconds needed to
travel one mile to miles per hour.
- Correct Usage of Equal and Equivalent in Math Statements [02/20/2008]
Is there a mathematical difference between "equal" and "equivalent"?
- Cramer's Rule in Action [05/08/1998]
Explaining Cramer's Rule by applying it to a system of equations.
- Cube and Square Roots [3/1/1995]
What is the sum of the cubes of the roots of 3x^3 + 4x + 2 = 0, and
simplify sqrt(3-sqrt(5))/(sqrt(2) + sqrt(7-3sqrt(5))?
- Cubic Equations [01/19/1998]
How would you solve a problem like 3x^3+x^2+15x+27 = 0?
- Cubic Equations [05/17/2001]
How do you solve cubic equations? Is there a general formula?
- Cubic Functions [5/13/1996]
Investigate the cubic functions of f(x) = ax^3+bx^2+cx+d...
- Cycling Motion Problem [6/26/1996]
A cyclist travels from A to B over a high pass...
- Cycling Uphill [7/8/1996]
I don't know how to handle the unknown speed at which the cyclist travels
- Dealing with Duplicate Elements [05/17/2002]
I need to develop a general formula to calculate the number of
different 'words' that can be formed from an N letter word where
some of the letters may be duplicated.
- DEFABC = 6(ABCDEF) [12/10/2001]
Let abcdef be a 6-digit integer such that defabc is 6 times the value of
abcdef. Find the value of a + b + c + d + e + f.
- Definition of 'Solve' [11/29/2005]
In algebra class I was told that a problem such as 2 + 2 cannot be
solved. In order to 'solve' a problem there has to be a variable
involved. Is this correct?
- Delivering a Message [09/02/2000]
A 25-mile long column of soldiers marches 25 miles. As the march begins,
a messenger starts at the rear of the column and goes forward...
- Derivation of Quadratic Formula [6/12/1996]
I would like to derive the solution to ax(2) + bx + c = 0.
- Derivations of Heron's Formula [11/24/1998]
How is Heron's formula (Hero's formula) derived?
- Deriving the Hyperbola Formula [04/27/1998]
When speaking of hyperbolas, why does C^2 = A^2 + B^2?
- Deriving the Quadratic Formula [10/15/1998]
How do you derive the quadratic formula from ax^2 + bx + c = 0?
- Diagram to Prove Difference of Squares Formula [06/18/2008]
I was able to make a picture showing why (a+b)^2 = a^2 + 2ab + b^2 by
having a square with sides a+b and getting four areas within the
square. But I can't figure out how to show that a^2 - b^2 =
(a+b)(a-b) using a similar diagram.
- Difference in Radius, Difference in Speed [06/25/2002]
What is the difference in speed between a point on the tread of a tire
and another point closer to the center, if the tire is rotating at
- Difference of Squares of Two Integers [7/2/1996]
Which positive integers can be written as the difference of the squares
of two integers?
- Difference of Two Cubes [11/18/1996]
What two positive integers satisfy the condition that the difference of
their cubes is 56,765?
- The Difference of Two Squares [9/21/1995]
In the following problem, I factor the same problem two different ways.
Why do I not get the same answer?
- Difference of Two Squares [08/17/1997]
Prove that every cube can be expressed as the difference of two squares.
- The Difference of x and y... [06/05/2003]
The difference of a number and its square is 42. Is the equation x^2 -
x = 42 or x - x^2 = 42?
- Different Approach to a Set of Equations [11/13/2002]
The sum of four numbers is 22. The first number is twice the
difference of the second and the fourth. The second number is five
times the difference of the third and the fourth. The third number
is twice the difference of the first and the fourth. What are the
- Differentiability, Intervals, Inflection Points of Piecewise Function [05/13/1998]
For what values of k and p will the function be continuous and
differentiable? On what interval will it be increasing? Find all points
- Digit Reversal Trick Explained [03/23/2001]
Take a 3-digit number and subtract its reverse. Then, take the result and
add its reverse. Why is the answer is always 1089, no matter what the
initial numbers were?
- Dilation Designation: Why in the Family of Trigonometric Functions Rather than Quadratics? [09/08/2016]
An adult wonders why horizontal dilation falls under trigonometry rather
than, say, under quadratic function families: is there something inherent to
quadratics that makes such scale factoring redundant? Doctor Peterson algebraically isolates the multiplier, interprets what happens — and reveals the associativity at the heart of the matter.
- Diophantine Equations, Apples, Bananas [06/08/1997]
Mick has $5.63 worth of bananas and apples. Bananas are 13 cents each and
apples are 7 cents each. How many different combinations of apples and
bananas can he have and what are they?
- Direct and Inverse Variation in One Problem [03/23/2006]
If s varies directly as r and inversely as t, and s = 10 when r = 5
and t = 3, for what value of t will s = 3 when r = 4?
- The Discriminant of Quadratic Equations [08/06/1998]
Can you explain more about the discriminant, b^2 - 4ac? Why is it
sometimes represented by a triangle (delta)?
- Discriminants [10/22/1996]
Find the discriminant and determine the nature and the number of roots of
2x^2+x-6 = 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.