See also the
Dr. Math FAQ:
order of operations
3D and higher
Browse Middle School Algebra
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Direct and indirect variation.
Inequalities and negative numbers.
Positive/negative integer rules.
Solving simple linear equations.
- 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
- Digit Problems: Find the Number [01/29/1998]
A two-digit number is 6 more than 4 times the sum of its digits. The
digits from left to right are consecutive even integers. Find the number.
- 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?
- Dimensions of a Rectangle [8/26/1996]
Find the original dimensions of a rectangle whose area is increased by 81
- Direct and Inverse Variation [04/25/2001]
An example of each type of problem.
- 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)?
- Distance Between a Point and a Line [08/23/1998]
Find the distance between the origin and the line 3x + 4y = 5.
- Distance, Time and Speed [8/1/1996]
What distance is traveled by driving 45 minutes at an average speed of 76
- 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 [12/11/1997]
What is the distributive property?
- 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).
- The Divide between Numbers and Variables [04/25/2011]
An adult student wonders why subtracting the coefficient from a variable expression would not eliminate it. Describing algebraic manipulations as processes of doing and undoing, Doctor Peterson clears up the confusion, and offers some further rules of thumb on simplification.
- Dividing a Square [07/31/1999]
A large square is divided into several equal-sized smaller squares using
x lines. How can I find a formula for the number of smaller squares
- Dividing Compound Fractions [11/16/1999]
Can you give me a simple step-by-step method to simplify expressions like
[(3/y)+(5/zy^2)] / [(5/2y)-(4/y^2)]?
- Division of Number Line [5/14/1996]
Using the interval from zero to one, how do I explain that when you find
half the distance and then half of that distance and so on, you'll never
settle on one number?
- 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?
- Empty Sets [08/15/1997]
Can you help me understand empty sets?
- Equal Sum, Product, Quotient of Two Numbers [10/13/2002]
I need to know the sum, product, and quotient, all equal, of two
- 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 x-intercept of 8.
- Equation in One Variable [04/13/1997]
How do I solve an equation in one variable by adding and subtracting
- Equations Involving Fractions [07/07/2000]
How do I solve equations with fractions and decimals in them?
- Equations That Make No Sense [01/15/2003]
Solve for x: x-8/5 = 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
- Equations with Fractions [04/21/1997]
How do you solve x/2 + x/3 = 1/6?
- Equation vs. Expression [03/19/1999]
How is an algebraic equation different from an algebraic expression?
- Equation with Absolute Value [3/25/1996]
I have problems solving equations with absolute value and graphing on a
number line. Example: |2n-6| > 5
- Equivalent Expressions / Equivalent Equations [07/27/1997]
Could you please explain the difference between equivalent expressions
and equivalent equations?
- Etymologies of Algebra, Geometry, Trigonometry [10/22/2001]
What are the origins and roots of the words geometry, algebra, and
- Evaluating an Expression [03/28/2001]
How do you evaluate an expression like 2x + 3x + 4, when x = 6?
- Evaluating Expressions [08/12/1997]
Evaluate the variable expression 5x and 13-x when x = 4.
- 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...
- Expanding Polynomials [06/16/1999]
How can you expand three binomials like (s+4)(2s-1)(s-2), or trinomials
like (z2-2z+3)(2z2+z-1)? FOIL doesn't work on these.
- Extraneous Solutions [08/08/2003]
What should an engineer interpret from an equation, or the solutions
of that equation, if its solutions prove to be extraneous?
- Factor and Multiply to Check [5/21/1996]
Is x to the second power plus 6x plus 5 factorable?
- Factor for X; Consecutive Odd Integers [01/19/1998]
(x-2)(x+3) = 6 : solve by factoring for x. Label your variables, write an
equation, solve, label answers...
- Factorials and Order of Operations [09/21/2000]
Where do factorials go in the order of operations?