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.
- Solving an Equation with two Variables [11/20/1995]
The problem is n + n + 5 = 25. How do I do this? It has two variables.
- Solving a Rational Inequality [11/15/2004]
How do you solve a rational inequality like (x-1)/(x+3) < 3?
- Solving a System of Three Equations in Three Variables [06/23/2007]
How can I find values of x, y, and z that make all three of these
equations true: x + y + z = 10, x - 2y + z = -2, and x - y - z = -12?
- Solving a Typical Rate-Time-Distance Problem [09/02/2005]
A look at how to use algebra to solve problems involving rates, times,
and distances. The problem in this example centers around walking and
running at two different rates for a total of 3 hours.
- Solving Equations [9/3/1995]
If n=x^2+y then how can you work out x if you know n and y, and work out
y knowing n and x?
- Solving Equations [3/23/1996]
A student has a number of 'word problems' that require solving equations.
- Solving Equations [01/15/1998]
Please help me solve these equations: x2+y = 31; y2+x = 41.
- Solving Equations for Variables [02/03/2002]
How do you solve the following equation for (M) and then (m)? k = M-m/
- Solving Equations that Equal Zero [02/26/1997]
How do you solve an equation like (5x+10)(7x-2) = 0?
- Solving Equations to Find Profit [8/10/1996]
You buy A and B for 40,000 Won; sell A for a 0.3 percent and B at a 0.2
percent discount. You profit 5000 Won - what was the original price of A?
- Solving Equations with Square Roots [03/28/2003]
When solving x + 1 = sqrt(x + 3), we can square both sides then solve
the equation; however, we get an extra solution that doesn't work. Why?
- Solving for b [05/10/2000]
When solving 10 + 2*sqrt(b) = 0 we get b = 25, but when we insert 25 into
the equation, we end up with 20 = 0. What are we doing wrong?
- Solving for X [01/13/1997]
Solve for x in 3(x*x)-2x+2 = 2/(3(x*x)-2x+1).
- Solving for x [1/23/1996]
I need help on this problem: x/x+4 = x+1/x+8
- Solving for x with Fractions [9/9/1996]
How do I solve this: 5/2 = 3/2 - x ?
- Solving Inequalities [12/10/1996]
How do you solve 6(m-4)-2(m+2) is less than 7(m-4)-6 ?
- Solving Inequalities with a Balance Scale Analogy [08/31/1998]
How do you graph these inequalities...?
- Solving Inequalities with Absolute Values [09/16/1998]
Can you explain two different ways to solve inequalities with absolute
- Solving Linear Equations [03/18/1997]
What are the steps to solve linear equations?
- Solving Linear Equations without PEMDAS [08/13/2002]
Is there a linear equation that can be solved using both the PEMDAS
order of operations and NOT using the order of operations and still
come out with the same answer?
- Solving Linear Inequalities: Picture a Number Line — or Several of Them ... [06/10/1999]
How can I solve 9 <= 2x-1 <= 15 for x?
- Solving Literal Equations [09/08/2001]
I can do equations fine with just numbers, but doing them literally with
letters is confusing me.
- Solving Pairs of Equations by Substitution [11/26/1997]
x + 3y = - 5; 3x - 2y = 7.
- Solving Quadratic Equations [03/07/1997]
A rectangle has an area of 80 square units. Its length is one more than
three times its width. What are the dimensions of the rectangle?
- Solving Quadratic Equations [9/14/1996]
3x^2 + x - 14 = 0? x^2 - 6x + 8 = 0?
- Solving Simple Equations [02/23/1998]
Equations like 3(30+s) = 4(s+19) and others following the same form.
- Solving Single Variable Equations [02/02/1997]
How do you solve equations like 4g + 7 = 35?
- Solving Systems of Equations Graphically and Algebraically [05/01/1998]
Graphing the system of equations y = -x and y = 2x, and indicating how
many solutions it has.
- Solving Systems of Linear Equations [02/09/1999]
Can you help me solve simultaneous equations?
- Solving x-(-16) = 0 [02/17/1998]
How do you solve: x- -16 = -16?
- Solving -X = 3 [10/26/1998]
How do you solve -X = 3? How can a negative equal a positive?
- Speed of Two Trains [7/31/1996]
A train leaves Chicago for Indianapolis, 216 km away, at 9 a.m. One hour
later, a train leaves Indianapolis for Chicago.... find the speed of each
- Square Roots in Equations [06/12/1997]
When do you take the square root in: 2(x-4)^2 - 3 = 13 ?
- Step-by-step Solution of Equation in One Variable [05/13/1998]
Commutative, associative, distributive, and other laws of arithmetic
applied to solve w in the equation 2 - 2(w + 6) = 2(w + 5).
- Straight Line on the Graph [09/10/1998]
Let f(x) = ae^(kx) where a>0 and k are constants. Show that the graph of
y = ln(f(x)) is a straight line.
- Strategy: Finding a Formula [11/14/1997]
Jill needs three pieces of lumber a total of 27 ft. long for a dog pen.
The second piece has to be 4 ft. longer than the first and the third 4
ft. longer than the second...
- Substituting Parameters for Numbers [11/29/2001]
I don't know what to do with both sides of the equation 17.20X/100 = X-
- Substituting Values for Variables [9/2/1996]
I know that a = -3/4 and b = -1/3. What's 2a+7b-ab/7a squared?
- Substitution Method [01/08/2002]
Here is the problem: 2x+y = 3, 3x+2y = 5.
- Subtracting as Adding a Negative [01/14/2002]
My teacher says to think of the question as a negative number, not a
minus number, but I don't know how he's doing that.