See also the
Dr. Math FAQ:
order of operations
3D and higher
Browse Middle School Equations
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Solving simple linear equations.
- Find the Equation of the Tangent Line [1/21/1996]
Find the the equation of the tangent line when x=1....
- Find the Numbers [08/28/2003]
One number is 61 more than a second number. The sum of the two
numbers is 127. Find the numbers.
- Formulas and Missing Quantities [10/09/2004]
Variations on the question "Could you drink enough water in a lifetime to empty a pool?" lead to a discussion of using formulas to find missing quantities.
- Formulas for the Equation of a Line [09/28/1998]
Can you explain the meaning behind the point-slope formula? What about
other formulas for the equation of a line?
- Fractional Coefficients [1/21/1996]
x-4/8 - 5-2x/3 = 7/12 ?
- General Strategies on Solving Linear Algebraic Equations [04/04/2005]
How do I solve equations like 12k + 15 = 35 + 2k? Is there a standard
rule to follow?
- Graphing Systems of Equations [06/01/1998]
How do you solve this system of equations by graphing: 3x + 2y = 5 and -
3x - 2y = 10?
- How Far Did the Plane Fly? [01/23/2003]
A plane flew 440km/h to its destination. It then flew 500km/h back. If
the whole trip took 9 hours, how far did the plane fly?
- How Many Coins Did Each Originally Have? [10/22/2001]
Natalie has some nickels, Dirk has some dimes, and Quincy has some
quarters. Dirk has five more dimes than Quincy has quarters... How many
coins did each originally have?
- How Many Mice, Cats, and Dogs? [01/13/2003]
You must spend $100 to buy 100 pets, choosing at least one of each
pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00
each, and dogs @ $15.00 each. How many mice, cats, and dogs must you
- Interpreting Slopes [09/14/1998]
Does the graph of each of these equations rise to the right, fall to the
right, is it horizontal, or is it vertical?
- Introduction to Linear Equations and Slope/Intercept Form [03/19/2005]
I'm an 8th grader, and I was looking at linear equations in your
algebra archives. I'm not sure what they are, so can you explain them
to me in a way that I can understand?
- Irrational Equations [06/02/2002]
I know what a rational equation is, but what's an irrational equation?
- I Solved It. Now What? [10/16/2003]
I can solve an equation like 12 = 5x + x + 6 to get x = 1, but I don't
know what it means, or what I'm supposed to do next.
- Linear Equations in One Variable [10/11/2001]
Solve: 35 = 17 + 3(x-2).
- Manipulating a Formula Algebraically [06/15/2006]
How do you solve M = C(1 + r) for r?
- Missing Factors [01/29/1998]
I can not figure out how to find the two missing factors when given two
- Missing Terms [12/19/1994]
Find the missing terms: ?(?-3)=5w-15 I don't understand how you
get the answer - what exactly is it looking for?
- Mixture Problem [11/11/1997]
How much pure antifreeze should be added to 3 gallons of a 30 percent
antifreeze solution to get 65 percent antifreeze?
- More Variables Than Equations in a System [01/21/2002]
I have a problem that uses four variables but only two equations to
relate them. I don't seem to have enough information to figure out
the value of each variable or answer the question. Can you help?
- A Mule and a Donkey [04/08/1999]
A famous Euclidean brainteaser.
- Multiplying Fractions [1/9/1998]
What times 20 equals 16?
- Multiplying or Dividing by a Negative Number [04/08/1999]
When x(x-4) is less than 0...
- Nonsense Solutions to Word Problems [04/28/2003]
Bill, Simon, and John are brothers. Bill is as many years younger than
one brother as he is older than the other. Simon is 7 years younger
than twice the age of John. John is 5 years older than half the age
of one of his brothers. I keep getting -3 for Simon's age. What am I
- Order in Linear Expressions [11/20/2001]
Can you give me a convincing argument as to why, in an equation such as
y=13-7x, where y is a function of x, it should be written as y=-7x+13?
- Order of Operations and Solving Linear Equations [03/01/2006]
When solving an equation like 2x - 3 = 5, why do we add 3 first and
then divide by 2? Why do equations not follow PEMDAS rules, which
would suggest that we should divide before adding?
- Parallel and Perpendicular Lines [01/14/1999]
How do you tell without graphing whether the graphs of these equations
are parallel, perpendicular, or neither?
- Plus or Minus Sign [03/08/2002]
What does this equation mean: y = +- k ? The - sign is directly under the
- Population and Percentage [03/07/1999]
Given population data, find the number of women in two different years.
- Pre-Algebra problem [11/11/1994]
How would you go about helping a typical 7th grade student with this
problem? -3n + 65 = -40 - 7n
- Probate Puzzle [12/15/2003]
A will specifies that every son should receive three times as much as
a daughter and every daughter should get two times as much as their
mother. What is the mother's share?
- Quadratic Equation [04/08/1997]
The sum of two numbers is 15 and their product is 54. Find the numbers...
- Quadratic Equation [7/10/1996]
Why is a quadratic equation "quadratic"?
- Quadratic Equations [12/3/1995]
My students want to know why an equation of the second degree is referred
to as a quadratic equation. What does the prefix quad have to do with
second degree equations?
- A Quadratic Word Problem [07/27/1999]
If the robbery rate per 1000 persons is increased by two and then
decreased by 6, the product of the rate increased by 2 and the rate
decreased by 6 is 180. What is the rate?
- Raising Both Sides of an Inequality to a Power [06/19/2006]
You have to flip the sign in an inequality if you multiply both sides
by a negative number. Is there any rule that says when you have to
flip the sign if you raise both sides to a power?
- Raising Sides of an Equation to the 0 Power [12/04/1997]
If you raise both sides of an equation to the 0 power, will both sides
then be equal to one?
- Rearranging an Equation [3/25/1996]
Rearrange the formula E=1/2mv to make v the subject.
- Rearranging an Equation [05/01/1999]
Solve for x in terms of y: y = (900x)/(2+x).
- The Secret to Mathematics? [09/27/2004]
I understand how to divide fractions--invert and multiply--but what if
the dividend or divisor is a variable?