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.
- Different Ways of Solving Systems of Linear Equations [10/28/2002]
Solving systems of equations by inspection, elimination, substitution,
intersection, or graphing.
- Find Equation for Two Points [12/12/2002]
I want to know how to find an equation for two given coordinate
- Finding the Equation of a Line [01/08/1997]
Given either a point and a slope or two points, how do you find the
equation of a line in both point-slope and standard form?
- Multiple Step Equations [12/7/1994]
I am having problems with math problems like:
29+q = -2(q-13) and -
2(c+7)-30 = 9c. Please help.
- Negative Numbers in Equations [11/20/2001]
I don't know how to do some of the homework I am getting. Here are some
examples of confusing equations: -30 = -37+b/15; -c/4-8 = -48.
- Perpendicular/Parallel Lines [01/17/1997]
Given the slope intercept form of a line, how do you find lines that are
parallel or perpendicular to it?
- Pre-Algebra: Equations and Other Tips [08/30/1997]
I'm in 8th Grade; can you give me tips on equations and other things that
will be useful for me to know?
- Simple Equation [8/20/1995]
2*2 + 24x = 23 + 1 - 11
- Simultaneous Equations [11/18/1994]
2y+10x=180; 4x+4y=100. Please explain how you do this system.
- Solving an Algebra Equation [3/20/1996]
I hope you will be able to help me with this problem: 10-(k+5) =
- Solving an Equation [11/30/2002]
Applying inverses to solve an equation.
- Solving an Equation in One Variable [12/20/1995]
I need you to go step by step with me so I don't miss anything:
2(x+4) - 1 = 3 + 4(x-1)
- Solving Equations [01/25/1997]
How do you solve equations like n/4 + 6 = -3?
- Substituting in Linear Equations [11/14/2001]
I am given two equations, 2y = 5x + 8x and 3y = 4x + 9x, and told to
substitute something. What should I do?
- Substitution and Elimination [01/13/2002]
Could you please explain substitution and elimination to me step by step?
- 10% Sodium + 30% Sodium [07/09/2003]
A group of chemists are conducting an experiment to produce a new
liquid material. One chemical contains 15% sodium (Na) and the other
chemical contains 30% sodium (Na). Once they mix the two samples the
resulting chemical contains 22% sodium (Na). How many milliliters
(ml) of each sample must be mixed to obtain 600 ml of the new
- 3 Equations, 3 Variables [01/26/1998]
How do you solve a system of three equations in three variables?
- Algebra as a Metaphor for Life [06/11/2002]
I've been given 'proofs' that -1 = 1, and that 2 > 4. Can you show me
why they aren't true?
- Algebra/Point-Slope [01/09/1998]
Can you explain how to do point-slope equations?
- Algebra - Solving Equations [11/03/1997]
I am having a hard time solving some of my algebra problems...
- Averaging Speeds of Individual Laps [12/12/2003]
A driver drives four laps around a track at 10, 20, 30, and 60 km per
hour. What is his average speed?
- Baseballs, Buckets, and Milk Cartons [10/09/2001]
The mass of a baseball is 50g. What is the mass of a bucket when 2
buckets = 6 blocks; 1 bucket + 1 block = 2 milk cartons; and 2 baseballs
= 1 milk carton.
- Changing Equations To Slope-Intercept Form [07/17/1998]
Can you explain how to change equations into slope-intercept form? For
example, 12(2x-1) - 5(3y+2) = 8?
- Clearing Fractions in an Equation [01/13/2005]
How do I clear the fractions in 1/4(8y + 4) - 17 = -1/2(4y - 8)? I
know I need to multiply by 4, but I get confused with all the
parentheses involved in doing that.
- Combining Rates of Work [08/30/1998]
It takes me 3 hours to paint a house. It takes you 5 hours to paint a
house. How long will it take for both of us to paint a house?
- Comparing Running Rates [01/20/2005]
Jack and Jane ran the 100 yard dash. When Jane won, Jack was 10 yards
behind her. They raced again, but this time Jane started 10 yards
behind the starting line. If they both ran at the same rate as in the
first race, who won the second race?
- Density of a Stone [09/14/2002]
A stone having a mass of 160 g displaces the level of water in a
cylinder by 30 mL. Find the density of the stone.
- Diameter Endpoint [01/26/2003]
The center of a circle is (-4,7) and one endpoint of a diameter is
(2,-1). What is the other endpoint of the diameter?
- 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?
- Digital Riddle [10/04/2016]
A non-native English speaker struggles to parse the clues in a riddle. After unpacking the verbiage step by step, Doctor Peterson offers general suggestions for approaching such place value puzzles.
- Distributive Double Duty [04/05/2016]
A teen seeks to solve a single-variable equation without computing the
common denominator of its many fractions. Doctor Greenie reveals a
pattern and provides a shifty hint, then applies the distributive
property twice to easily deduce the solution.
- Doing the Same Thing to Both Sides of an Equation [10/20/2003]
When I subtract something from one side of an equation do I add it to
the other side or do I subtract it from that side also?
- Elimination Method in Real Life [03/30/2003]
If 3 tall candles and 5 small candles cost $7.30, and 2 tall candles
and 2 small candles cost $3.40, how much does 1 tall candle cost? How
much does 1 small candle cost?
- 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 Manipulation [4/13/1996]
If m and n are integers, which of the following could be equal to (mr +
ns)^2 for all values of r and s?
- Equations! [5/2/1995]
Can you solve x + y = 5, xy = 3, and x^2 + y^2 = ?
- Equations and Negatives [05/23/1999]
How would I solve the following problem: 6(-N) = 3(N)+72 ?
- Equations That Make No Sense [01/15/2003]
Solve for x: x-8/5 = x+2/6.
- Equations Versus Formulas: Their Unknowns, Substitutions, and Solutions [03/12/2016]
A teen wonders if formulas have more unknowns than equations do; or if
you substitute into formulas, but solve equations. With examples
aplenty, Doctor Peterson clarifies and unpacks the terms.
- Equations with Fractions: 7y/9+2 = 2y/3 [11/23/1997]
First I moved the variables to one side and the numbers to the other, but
I always ended up with -18/13.